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LABORATORY EXERCISES IN PHYSICS 



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Laboratory table, shown in isometric projection. 
Length, 6 ft. ; width, 3h ft. ; height of top, 3 ft. 
Height of cross-bar above top, 3 ft. 4 in. 



LABORATORY EXERCISES 



IN 



PHYSICS 



FOR SECONDARY SCHOOLS 



BY 



GEORGE R. TWISS, B.Sc. 

HEAD OF THE DEPARTMENT OF SCIENCE IN THE CENTRAL 
HIGH SCHOOL, CLEVELAND, OHIO 



THE MACMILLAN COMPANY 

LONDON: MACMILLAN & CO., Ltd. 
1902 

All rights reserved 



THE LIBRARY OF 

OONORSSS, 
Tvwo Cop.ee Received 

OCT. 31 '902 

CLASSCX-*Xc. No 
GOPY J3 






Copyright, 1902, 
By THE MACMILLAN COMPANY. 



Set up and electrotyped October, 1902. 



Norfajooti ^ress 

J. S. Cushing & Co. — Berwick & Smith 
Norwood Mass. U-S-A. 



PREFACE 

The practicability and usefulness of these exer- 
cises, in connection with a course in elementary- 
general physics, have been demonstrated by the test 
of actual use in the form of mimeographed sheets 
during a period of several years. They have reached 
their present form through a succession of revisions 
suggested by the needs of the author's pupils. 

His classes have been large, they have represented 
both sexes and all grades of natural ability, and 
they have been limited by the school programme to 
working periods of forty-five minutes. The direc- 
tions, worked out under these difficult conditions, 
have proved satisfactory. 

Within the past two years the sheets have come 
into the hands of physics teachers in other and 
smaller schools, who have found them adapted to 
their needs also, and have encouraged the writer 
to prepare them for publication. 

The experiments are selected and the directions 
written with regard to three purposes : first, to 
secure the thorough enforcement of some of the 
fundamental principles of the science, together with 
a View of the kind of thinking and experimentation 
by means of which the facts and principles of physics 



vi PREFACE 

have been established ; second, to develop habits of 
precision in observation, thought, and expression ; 
and third, to train the student in the acquisition of 
practical power and skill in the use of apparatus. 

The author believes that physics, being a body 
of organized truth logically connected throughout, 
should be taught as such, — not as a collection of 
unrelated facts, or of facts only incidentally related. 
Therefore, in common with many other teachers of 
physics and with the authors of some of the best 
secondary text-books, he thinks that the laboratory 
experiments should be logically and intimately con- 
nected in a well-constructed teaching plan, which 
includes thorough text-book and recitation work, 
and also oral explanation with demonstrations at the 
lecture table. The plan should be so carried out 
that the student proceeds step by step from facts 
and principles that are already part of his mental 
property to those that are new to him. 

Accordingly, while the exercises of this manual 
are mostly quantitative and every one sufficiently 
exacting for the last two of the three purposes stated 
above, they are rigidly restricted to those which 
have been found especially useful in giving second- 
ary students a mastery of some of the great general 
principles which belong to the framework of the 
science. The teaching of principles by observation 
and induction, by deduction and experimental veri- 
fication, is the controlling idea. To this end the 
laboratory exercise is but a means. To make it *an 
end in itself is obviously a serious mistake. 



PBEFACE vii 

Attention is respectfully directed to the following 
features of the work, which it is hoped will commend 
it for special consideration : — 

1. Copious paragraph references at the head of 
each exercise direct the student to the co-related 
text of the most widely used modern class-books in 
physics. 

2. Each exercise begins with a clear and concise 
statement of the purpose that it is intended to 
accomplish. 

3. The directions for manipulation are meant to 
be concise, yet so clear and explicit that the student 
will rarely need to seek assistance elsewhere as far 
as mere manipulation is concerned. If he asks a 
question about operations, he can be sent back to 
these directions with great profit to his own inde- 
pendence and with a saving of much energy to the 
instructor, who can thus devote his time to the 
teaching of the subject instead of to profitless repe- 
tion of experimental details. 

4. Pointed questions are frequently introduced to 
direct the observation and thought of the pupil 
while experimenting. 

5. In drawing his inferences and reaching his 
conclusions, the student is aided by directions and 
questions which enable him to get over the difficult 
steps, and make the path plain so that he can pro- 
ceed alone where it is less difficult. 

6. Directions and suggestions are given for the 
form of record, carried out so as to train the student 
to the habit of arranging his notes in a manner such 



Vlll PREFACE 

that the contents can be easily referred to by himself 
and easily inspected by the teacher. 

7. Due consideration is given the experimental 
errors of each exercise. Great precision is not pos- 
sible in classes of beginners ; but a careful considera- 
tion of the causes and limits of the more important 
errors gives a very valuable training in connection 
with observations which are only fairly accurate. 

8. At the end of each exercise the student is 
directed to state the principle verified, or the con- 
clusion reached, or the lessons learned from the 
experiment. Thus he is to begin with a definite 
purpose and to end with stating what he has ac- 
complished. 

9. Tables of physical constants and information 
for the teacher (who can easily get it elsewhere) are 
purposely omitted from the manual, which is intended 
for the pupil. 

10. The number of exercises presented is smaller 
than in most of the manuals hitherto published. It 
is not attempted to give work illustrating every 
principle, nor to multiply methods of reaching a 
given result. 

Thirty or thirty-five exercises selected equitably 
from the different parts of the subject is a number 
amply sufficient to secure the kind of training that 
the laboratory is designed to give. A small number 
of exercises worked " for all there is in them " is 
better than a large number carelessly and super- 
ficially performed. This is an idea which the author 
believes is growing in favor ; and he has tried to be 



PBEFACE ix 

in line with the reaction, which is surely coming, 
against overloaded text-books and manuals. Out of 
the forty-three exercises of this manual he has been 
wont to omit from seven to ten, dropping different 
ones in successive years. 

Teachers will find much information that is nearly 
indispensable to them in any of the books of the fol- 
lowing list : — 

Elementary Practical Physics. Stewart & Gee. 3 vols. $4.85. 
The Mac mill an Company. 

Physical Manipulation. Pickering. 2 vols. $7.00. Hough- 
ton, Mifflin & Co. 

Laboratory Arts. Threlf all. $1.50. The Macmillan Company. 

The C. G. S. System of Units. Everett. $1.25. The Mac- 
millan Company. 

Instructions to Voluntary Observers. U. S. Weather Bureau. 

The Barometer. U. S. Weather Bureau. 

Methods of Glass Blowing. Shenstone. $0.80. Longmans 
&Co. 

It gives me pleasure to acknowledge my indebt- 
edness to my friend, Mr. Franklin Turner Jones, 
teacher of physics and chemistry in the South High 
School of Cleveland, who has read the work in 
manuscript and made many valuable and practical 
suggestions. 

I am also much indebted to Professor Frank Per- 
kins Whitman, of Western Reserve University, who 
has been kind enough to read the book in the proof- 
sheets, and to make some criticisms of which I have 
been glad to avail myself. Although I have used 



X PBEFACE 

all possible care to avoid mistakes and inconsisten- 
cies, any that may be found uncorrected must be 
laid at my own door. 

My thanks are due several firms for the loan of 
electrotypes, or for permission to reproduce cuts 
from their catalogues. Figures 11, 18, 26, 38, and 
40 are from the L. E. Knott Apparatus Co., Boston; 
24 and 31a, from William Gaertner & Co., Chicago ; 
29 and 32, from J. R. Brown & Sharpe, Providence. 
Figure 5 is from Fairbanks, Morse & Co., Chicago; 
16, from Henry J. Green, Brooklyn ; 25, from the Chi- 
cago Laboratory Supply and Scale Co. ; and 27, from 
Thomas W. Gleeson, Boston. Figures 35, 36, and 
37 were kindly loaned by The Macmillan Company, 
from D. C. and J. P. Jackson's " Elementary Elec- 
tricity and Magnetism." The originals of all the 
other cuts were drawn by myself, expressly for this 
book. 

Suggestions and corrections from teachers using 
this manual will be greatly appreciated by the 
author, who will also be pleased to answer inquiries 
in regard to the exercises, or to the equipment and 
management of the laboratory. A small pamphlet 
containing such information as may be required by 
teachers in connection with the use of this book will 
be issued in case there appears a demand for it. 

GEORGE R. TWISS. 

Central High School, 
Cleveland, Ohio, 
September 1, 1902. 



CONTENTS 

TO THE STUDENT 

PAGE 

The Laboratory xv 

Directions for making Notes xviii 

Text-book References xxi 

Reference Books xxii 

CHAPTER I 
Measurements 

EXERCISE 

1. Length Measurement 1 

2. Determination of Volume 5 

Part A. By Calipers and Rule 6 

Part B. By the Vernier Slide Caliper ... 7 

Part C. By Submersion in a Graduate ... 9 

3. Determination of Mass by Weighing .... 10 
Supplementary to Exercises 2 and 3. Density . . 15 

CHAPTER II 
Mechanics or Solids 

4. Comparison of Masses by the Acceleration Method . . 16 

5. Concurrent Forces 21 

6. Parallel Eorces and the Law of Moments . . ..27 

7. Centre of Mass 31 

8. Weight of a Bar. Law of Moments .... 33 

9. Work. Inclined Plane 37 

10. Inclined Plane (continued) 40 

11. Laws of the Pendulum 42 

Part A. Effect of Length and Amplitude ... 42 

Part B. Acceleration of Gravity .... 48 
Part C. Graphic Representation of the Law of Length 

and Period 49 

Part D. Mass and Period 52 

xi 



Xll 



CONTENTS 



CHAPTER III 
Mechanics of Fluids 

EXERCISE PAGE 

12. Relative Density by the Submersion Method ... 54 

Part A. Of a Solid 54 

Part B. Of a Liquid . . . . . . .56 

13. Relative Density by the Flotation Method ... 59 

Part A. Of a Solid . . . . ... 60 

Part B. Of a Liquid . 62 

14. Relative Density of a Liquid by Hare's Method . . 65 
Barometer . .69 

15. Boyle's Law 71 

Part A. Verification 71 

Part B. Graphic Representation .... 74 

CHAPTER IV 
Heat 

16. Thermometer 77 

17. Specific Heat 82 

18. Latent Heat of Fusion 87 

19. Latent Heat of Vaporization . . . . . .91 



CHAPTER V 
Magnetism and Electricity 

20. Lines of Magnetic Force . 

21. Field of Electromagnetic Force 

22. Simple Voltaic Cell 
Galvanometers . 
Commutator 
Shunts 
Micrometer Caliper 

23. Electrical Resistance 

Part A. Use of Wheatstone's Bridge 

Part B. Law of Resistance and Length 

Part C. Law of Resistance and Sectional Area 

Part D. Resistivity 



96 
100 
103 
107 
112 
113 
113 
116 
119 
121 
123 
124 



CONTENTS 



Xlll 



EXEBCISE 

24. Measurement of Current Strength 

25. Short Distance Telegraphy 

26. Long Distance Telegraphy 

27. Induced Currents 



PAGE 

126 
133 
136 
139 



CHAPTER VI 

Sound 

28. Speed of Sound .... 

29. Vibration Frequency of a Tuning-fork 

30. Wave Length of a Tone . 

31. Cause of Overtones .... 

32. Laws of Vibrating Strings. Length 

33. Laws of Vibrating Strings. Tension 

34. Laws of Vibrating Strings. Diameter 



142 
145 

149 
152 
157 
160 
162 



CHAPTER VII 
Light 



35. Law of Inverse Squares. 

36. Law of Inverse Squares. 

tometer . 

37. Candle Power of a Lamp 

38. Regular Reflection . 

39. Image in a Mirror . 

40. Refractive Index 

41. Focal Length of a Lens 

42. Conjugate Foci of a Convex Lens 

43. Study of Spectra 



Bunsen's Photometer 
Alternative. Rumford's Pho- 



164 

168 
172 
173 
176 
178 
182 
185 
189 



TO THE STUDENT 

THE LABOEATOEY 

The laboratory is your workshop. The value of 
the work done in it will depend upon the faithfulness 
with which you follow out the directions of the in- 
structor and of this manual. 

Punctuality. — Be prompt in beginning and stop- 
ping work at the proper signals. The time is short, 
and you cannot afford to lose a minute. 

Attention. — Keep your attention fixed upon the 
work in hand, and listen carefully to every sugges- 
tion of the instructor. It is sometimes necessary to 
speak a few words to another student, but such con- 
versations should be limited to that which is abso- 
lutely essential and held in a low undertone, as is 
customary in public libraries or large offices. Other- 
wise confusion and disorder will distract attention 
of both pupils and teacher, and good work cannot 
be done. No trifling can be tolerated. The indi- 
vidual freedom which must be allowed pupils in the 
laboratory is so much greater than that which is 
customary in the class room and study room that 
you will often be strongly tempted to abuse it in 
such a way as seriously to interfere with your own 
work and that of others. The effort that you must 



xvi TO THE STUDENT 

make at self-control is one of the best features of 
the discipline that the laboratory training can give 
you. Do not compel the instructor to use repres- 
sive measures, but persist in governing yourself. 

Order. — Preserve an orderly arrangement of ap- 
paratus while working. See that things are in the 
positions where they can be used most conveniently 
and expeditiously. Good and systematic work can- 
not be done with appliances in confusion. 

Neatness. — Wipe off all dust from apparatus before 
beginning work. If the table or any piece of appa- 
ratus becomes soiled, or littered, or wet, it should be 
cleaned and dried immediately. See that you have 
dust cloths and a sponge at hand for the purpose. 
Do not leave papers or scraps of any kind upon the 
tables or floors, but deposit them in the receptacles 
provided. 

Explanations. — Questions about the work should 
be asked of the instructor and not of a fellow-student. 
The latter may cause you to lose time by setting you 
on the wrong track ; or he may deprive you of val- 
uable mental exercise by telling you what you are 
able to think out for yourself. 

Sinks. — Never throw anything into the sinks 
excepting water. 

Preparation. — Study very carefully each exercise 
before the laboratory hour in which it is to be per- 
formed. Do not try to commit directions to memory, 
but think out everything they tell you to do. Try 
to comprehend the plan of the work, and picture to 
yourself just how you will carry it through. Where 



TO THE STUDENT xvii 

your previous instruction by lecture and recitation 
work has prepared you for it, try also to think out 
the kind of results you may reasonably look for and 
the conclusions you may possibly reach. If the aim 
is to verify a law, see that you have the law well 
learned and know exactly what it means. 

Prepare the page upon which your notes are to be 
taken. Have tabular forms ruled and spaces allotted 
for the different kinds of notes, so that no time may 
be lost in the laboratory in deciding where to put 
them, or in doing any writing that can as well be 
done outside. Every minute of time in the labora- 
tory will be needed for the experimental work and 
the recording of the data there observed. 

Carefulness. — Your work will be valueless unless 
accurate. Use conscientious care in making all ob- 
servations. Obtain all values as accurately as is 
possible with the apparatus you are using. Record 
phenomena and numerical data at the moments when 
they are observed. This is very important. Record 
exactly what you observe, not what you think you 
should observe. Be absolutely and uncompromis- 
ingly honest with your own intellect, otherwise your 
time in the laboratory is almost thrown away. Do 
not nervously hurry, but work deliberately, steadily, 
and unremittingly, keeping the plan and purpose of 
the exercise constantly in mind. Eyes and hands 
should work together, both controlled by an alert 
mind. 



XVlll TO THE STUDENT 



DIRECTIONS FOE MAKING NOTES 

1. Write your name, room number, and hour of 
recitation on the outside of your note-book. 

2. Use the first page for a title-page and the next 
two for a table of contents in which you are to 
record the number of each exercise, together with 
its purpose or title, and the number of the page 
where it is recorded. 

3. Begin the notes for each exercise or experi- 
ment on a new page, and leave a margin at least 
1 cm. wide at each edge. 

4. Number each left-hand page and the corre- 
sponding right-hand page with the same serial num- 
ber; and at the top of each page place the date 
when the work is done. 

5. Enter upon the left-hand pages with sharp, 
hard pencil the purpose or aim of the exercise, all 
observations, numerical data (in tabular form), all 
calculations and results, together with as much con- 
cerning apparatus and operations as may be neces- 
sary to furnish a basis for a complete report of your 
experiment, which is to be entered in ink upon the 
corresponding right-hand page. The entries on the 
left-hand pages must be neatly and systematically 
arranged, without crowding, and, with the exception 
of purpose and calculations, no matter should be placed 
there except notes taken in the laboratory at the time 
when the observations are made. 

6. Enter in black ink, upon the right-hand page, 



TO THE STUDENT XIX 

a clear, concise, and complete record of the exercise 
under the headings given below. Do not copy the 
directions, but compose the record yourself. 

(a) Purpose. — Under this heading write a con- 
cise statement of what is to be accomplished by the 
exercise ; thus, " The purpose of this exercise is to 
determine the specific heat of a metal ; " or " The 
purpose of this exercise is to verify the law of 
Boyle." 

(6) Apparatus and Materials. — Under this head- 
ing record a list of all pieces of apparatus and all 
the materials used. Describe any unfamiliar piece, 
or any new arrangement. Many of the pieces are 
numbered ; and the number of each piece should be 
recorded, with its name, in order that it may be 
identified if it is to be used again. Make a diagram 
or sketch showing the parts of the apparatus and 
their arrangement while in use. The diagram should 
be neat and clear-cut, and its parts or points should 
be lettered. By referring to the lettered parts of the 
diagram the descriptions that follow can be much 
shortened. 

(c) Operations. — Under this heading record in 
clear, grammatical sentences in the indicative mode 
each act that you perform as an essential part of the 
experiment. Avoid all unnecessary words. Do not 
repeat in one place anything expressed or directly 
implied in another. Do not hesitate to use the pro- 
noun I (or we, if others worked with you). 

(d) Observations. — Here record everything that 
happens which may have any relation to the laws 



XX TO THE STUDENT 

or properties which you are studying in the experi- 
ment or any bearing upon the conclusions to be 
derived. Exclude everything that is irrelevant. 

(e) Numerical Data. — These should be recorded 
in neatly ruled tabular forms, different observed 
values of the same quantity in the same vertical col- 
umn, columns of related quantities near together, and 
each under its proper heading, so that the meanings 
of the numbers and their relations to each other can 
be taken in at a glance. Numerical quantities should 
never be incorporated in the text of your notes, but 
set apart conspicuously so that it will not be neces- 
sary to search for them. Final numerical results 
should be underlined with red ink, or otherwise 
made conspicuous ; and, if they are to be compared 
with others, should be placed near them. 

(/) Errors and Corrections. — Under this heading 
enumerate the sources of error pertaining to each 
part of the apparatus and each operation in turn ; 
and if corrections are to be made for these errors, 
indicate the method of correction and the reason 
for it. 

(#) Inferences or Lessons. — Under this heading 
state what you have learned by the experiment, to 
what conclusion you have come, or what inferences 
you can draw as a result of the, experimental study 
just completed. If the experiment was made to 
verify an established law, briefly explain upon what 
grounds you conclude that the law is verified by 
your results. 

7. Never make notes or calculations of any kind 



TO THE STUDENT XXI 

upon loose paper. Enter them all upon the left-hand 
pages of your note-book. The fundamental purpose 
of the note-book is the presentation of all such data 
in a form available for quick inspection by the 
teacher and ready reference by the student. 

8. Do not erase numerical data. Quantities which 
appear erroneous or valueless may prove worthy of 
consideration. Enclose rejected matter in brackets, 
and write " Rejected " at the side of it. 

9. Do not use common fractions. Express all 
fractional values in decimals. 

10. Do not crowd the notes. Leave blank space 
between the different sections of the written matter 
and make the headings prominent. 

TEXT-BOOK REFERENCES 

The text-books referred to by paragraph numbers 
at the beginning of each exercise are named below : — 

A . . . School Physics. Avery. Butler, Sheldon & Co. 

C . . . Elements of Physics. Crew. The Macmillan Com- 
pany. 

C & C . High School Physics. Carhart and Chute. Allyn & 
Bacon. 

GE . . Elements of Physics. Gage. Ginn & Co. 

GP . . Principles of Physics. Gage. Ginn & Co. 

H . . . A Brief Course in Physics. Hoadley. American 
Book Company. 

H & W . Elements of Physics. Henderson and Woodhull. 
D. Appleton & Co. 



xxii TO THE STUDENT 

J . . . Heat, Light, and Sound. Jones, D. E. The Mac- 
millan Company. 

J & J . Elementary Electricity and Magnetism. D. C. & 
J. P. Jackson. The Macmillan Company. 

L . . . Elementary Mechanics. Lodge. The Macmillan 
Company. 

S . . . Physics. Slate. The Macmillan Company. 

T . . . Elementary Lessons in Electricity and Magnetism. 
Thompson. The Macmillan Company. 

W & H . A Text-book of Physics. Wentworth and Hill. 
Ginn & Co. 



KEFERENCE BOOKS 

Students are earnestly urged to read as much as 
they can from the books in the following list. Parts 
of some of them are too difficult to be thoroughly- 
comprehended, but much of all of them is within 
reach of beginners, and will be of great assistance in 
extending the knowledge gained in the laboratory 
and class-room. A few of them can be read entire, 
and are sure to be not only inspiring, but fascinating 
as well. 

Mechanics. Lodge. The Macmillan Company. 
The Conservation of Energy. Stewart. D. Appleton & Co. 
Heat as a Mode of Motion. Tyndall. D. Appleton & Co. 
Lectures on Electricity. Tyndall. D. Appleton & Co. 
Lectures on Electricity. Forbes. Longmans & Co. 
Faraday as a Discoverer. Tyndall. D. Appleton & Co. 



TO THE STUDENT XXlll 

Elementary Electricity and Magnetism. D. C. and J. P. Jack- 
son. The Macmillan Company. 

Lessons in Electricity and Magnetism. S. P. Thompson. The 
Macmillan Company. 

The Indnction Coil in Practical Work. Wright. The Mac- 
millan Company. 

On Sound. Tyndall. D. Appleton & Co. 

The Theory of Sound in Relation to Music. Blaserna. D. Ap- 
pleton & Co. 

Sound. Mayer. D. Appleton & Co. 

Light. Mayer and Barnard. D. Appleton & Co. 

Light, Visible and Invisible. S. P. Thompson. The Macmil- 
lan Company. 

Six Lectures on Light. Tyndall. D. Appleton & Co. 

History of Physics. Cajori. The Macmillan Company. 

Experimental Science. Hopkins. Munn & Co. 



LABOKATOBY EXEECISES IN PHYSICS 



CHAPTER I 

MEASUREMENTS 

Exercise Number 1 
length measurement 



References 



A 17-20 
C 8, 9, 11 



C & C 7, 8 
GE 2, 4-5 



GP1, 2 
H 11-13 



H & W 36-43 
W & H 9, 10 



Purpose. — The purpose of this exercise is to 
measure the length of the laboratory table. 

Apparatus. — The apparatus consists of a meter 
rule, — graduated in centimeters (hundredths) and 
millimeters (thousandths) on one side, and in 
inches and eighths on the other, — a rectangular 
block, and a knife or pin. 

Operations. — 
(a) Place the 
block at one end 
of the table, 
with one of its 
plane surfaces ty 
perpendicular to 
the upper sur- 

p r . -i .it Fig. 1. — Showing the rule and block in 

face of the table. position. 




2 LABORATOBY EXERCISES IN PHYSICS 

(b) Stand directly in front of the block, set the 
rule on edge, and bring one of the centimeter lines 
on the rule (e.g. the line marked 1) into coincidence 
with the back edge of the block. 

(c) Adjust the rule parallel with edge of the table ; 
and see that the 1 cm. line is still in place. 

(<P) With the knife, make a short, thin scratch at 
the point where the 99 cm. line meets the surface of 
the table. 

(e) Move the rule along ; again adjust it parallel 
with the table top edge, but with the 1 cm. line at 
the knife scratch, and make a new knife scratch 
at the 99 cm. line. 

(/) Continue the process until the length of the 
table remaining to be measured is less than the 98 cm. 
of the rule ; then, in a similar manner, read off the 
number of centimeters in the remainder, using the 
block, as before, to determine the position of the other 
end of the table. 

(#) If the end of the table does not exactly coin- 
cide with one of the centimeter lines, note the number 
of additional millimeters between the nearest centi- 
meter line on the left, and the millimeter line with 
which it does coincide. 

If it does not coincide exactly with a millimeter 
line, estimate the fractional part of a millimeter re- 
maining as 0.5 mm., if it is nearer to the middle 
of the millimeter space than to either end of that 
space. If the end of the table is nearer to either 
end than to the middle of the millimeter space, read 
the number of whole millimeters between the last 



MEASUREMENTS 3 

centimeter line and the millimeter line with which 
it most nearly coincides. 

(K) Add up the numbers of centimeters and milli- 
meters to get the total length of the table, expressing 
it in meters, hundredths, and thousandths. 

For example, suppose that you have found it to be 
98 cm. + 98 cm. + 98 cm. + 7 cm. + 5 mm. + 0.5 mm.; 
the total is 301.55 cm. or 3.0155 m. 

(T) Make at least four more measurements in the 
same manner, at different distances from the front edge 
of the table ; enter the results under the others ; and 
find their average for the mean length of the table. 

(/) In another column enter an equal number of 
measurements, made in the same manner, but with 
the inch side of the rule. If there is a remainder, 
less than an inch, estimate its value to the \ part of 
the \ inch divisions (that is, to ■£% inch). Obtain 
the mean as before, reducing it to inches and a deci- 
mal fraction of an inch. 

(Jc) Reduce the mean value in inches and a decimal 
of an inch to meters and a decimal of a meter (divide 
by 39.37), and place the result beneath the mean 
value obtained with the metric side of the rule, so 
that these two mean values can be readily compared. 
If the work has been done with respectable accuracy, 
they will agree within 2 or 3 mm. 

The individual measurements will agree closely 
with each other. If they do not agree fairly well, this 
will indicate large errors, or mistakes caused by care- 
lessness, or that the table is slightly irregular in form. 

Precision of Statement. — In a physical experiment 



LABORATORY EXERCISES IN PHYSICS 



we should state the result numerically just as accu- 
rately as we are able to observe it. Hence, when we 
measure the thousandths of meters and estimate the 
ten-thousandths, we should retain the figure in the 
fourth decimal place, even though it be a zero. On 
the other hand, since this last figure represents a 
number of ten-thousandths that has been estimated, 
it is in doubt, and any that may follow it, being wholly 
unknown, should be rejected. In taking the mean of 
the individual measurements the same principle is to 
be observed. In this and all subsequent work, retain 
the first doubtful figure and reject all that follow. 

Data. — The following form for the record is sug- 
gested ; but the student should always try to devise 
for himself 
neat and con- 
venient forms 
for his results. 
The purpose 
of a record in 
tabular form 
is to make it 
easy to in- 
spect and 
compare the 
quan titie s 
that are re- 
lated to one 
another. 



Length of Table 



Side 1 



Measurement 


Meters 


Inches 


1 






9 






3 






4 






5 






Mean 







Mean Length (measured in meters) 

Mean Length (measured in inches 

and reduced) .... 

Difference .... 



in. 



m. 
m. 



1 In the blanks, place the number of the table and the side 
measured, e.g. Table Number 1, North Side. 



MEASUREMENTS 5 

Precautions. — (a) In reading a rule or scale of 
any kind, keep the line of sight perpendicular to the 
edge of the scale at the point of reading, in order 
to avoid the errors of parallax. 

(V) The first and last divisions of a scale, if at its 
ends, should not be used, as they are likely to be 
somewhat worn off. 

Lessons. — The exercise is designed to teach the 
principles which underlie the use of scales in simple 
linear measurements, and to give practice in the use 
of metric units. 

Additional Work. — If there is time for additional work, take 
a longer series of measurements, or measure the other three 
sides of the table, and from the mean length and mean width 
calculate the area in square meters. 

Note. — If it is desired not to scratch the table, the teacher 
may supply a squared board, to be laid on top. In that case 
the measurements should be made upon the board just as 
directed for the table top. 

Exercise Number 2 
determination of volume 





References 




A 20 


C & C 8 GP 6 


H & W 47-51 


C 12, 13 


GE 6 H 14, 16, 18 


W & H 10 



Purpose. — The purpose of this exercise is to 
determine the volume of a regular solid by three 
different methods : (a) by calipers and rule, (6) by 
the vernier slide caliper, and (<?) by submersion in 
a graduate. 



6 LABORATORY EXERCISES IN PHYSICS 

Part A 
BY CALIPERS AND RULE 

Apparatus. — A pair of calipers, a 30-centimeter 
rule, reading to millimeters, and a solid (say a 
cylinder of copper, brass, or aluminum) are used. 

Operations. — The mean altitude, a, and the mean 
diameter, 2 r, are to be determined by measurement, 
and the volume, V, is to be calculated by the rule 
of geometry, expressed in the formula, V=7rr 2 a. 
= 3.1416.) 

(a) Adjust the calipers so that their tips are just 
in contact with the opposite bases of the cylinder, 
the line joining the tips being parallel with the axis 
of the cylinder. 

(5) Remove the calipers, being careful not to 
allow the tips to change their relative positions; 
and apply the tips to the rule, so that the inside 
edge of one tip is at the middle of one of the 
centimeter lines, and the line joining the tips is 
parallel with the edge of the rule. Read the position 
of the inside edge of the other tip, to the tenth of a 
millimeter, and record the distance between the tips 
in centimeters, tenths, and hundredths. The hun- 
dredths of centimeters (tenths of millimeters) are to 
be estimated by the eye. This can easily be done ; 
thus, the smallest amount more than J is .6, less than 
■|, .7, and so on. 

(<?) In this manner, make and record at least five 
measurements of the altitude taken at different places. 

(c?) In a similar manner make the same number 
of measurements of the diameter, the lines between 



ME A S UREMEXTS 



the caliper tips being parallel with, the bases of the 
cylinder. 

(e) Record the individual measurements and their 
mean values in a tabular form similar to that used 
in Exercise 1. Compute and record the volume. 

Part B 

BY THE VERNIER SLIDE CALIPER 

Apparatus. — The additional apparatus is the ver- 
nier slide caliper. 

Operations. — Each dimension is to be measured at 
least twice ; the individual and mean values are to 
be recorded in tabular form as before; and the mean 
volume is to be computed. 

(a) Loosen the set screw, s; and, grasping the 
scale in the right hand, press the thumb against the 
little projection, _p, 
below the vernier 
till the movable jaw 
withdraws from the 
fixed one. Xow 
place the cylinder 
between the jaws; 




.ilnnlmilmU hliii.l.i.Il.mlinXuli 



Fig. 2. — Vernier Slide Caliper. 



and, with the thumb on the projection, press the 
jaws together against the two bases of the cylinder, 
so that they are just in contact with the respective 
bases. 

(5) By means of the set screw, fasten the movable 
jaw in position, remove the cylinder, and take the 
reading of the caliper in accordance with the rule 
that follows. 



8 LABORATORY EXERCISES IJST PHYSICS 

(c) To read the (metric') vernier slide caliper. — 
Read and record the number of centimeters and 
whole millimeters from the zero of the scale to the 
zero of the vernier ; and add the number of tenths 
of a millimeter in the remainder. This is denoted 
by the number of the line on the vernier which most 
nearly coincides with some line on the scale : e.g. if 
line number 3 on the vernier coincides with some 
line on the scale, the remainder is .3 mm. 

In order to understand why this is so, notice that the vernier 
scale is 9 mm. long and is divided into 10 equal parts ; hence, 
each vernier division is .9 mm. long. On the other hand each 
division of the fixed scale is 1.0 mm. long. Therefore when 
vernier line 3 coincides with some fixed scale line, vernier line 2 
falls .1 mm. short of the fixed scale line next to the left of it. 
It is obvious also that vernier line 1 must fall .2 mm. short of 
the fixed scale line next to the left of it. Finally the vernier 
line must fall .3 mm. short of the fixed scale line next to the 
left of it. But this space of .3 mm. is the fractional part of a 
millimeter that was to be measured. In general, if the coin- 
ciding vernier line is n, the distance from that line back to the 
vernier line is .9 n mm. ; and the distance back to the fixed 
scale line next to the left of the vernier line is n mm. Now, 
n — .9 n = n tenths mm., the fractional remainder that was to 
be measured by means of the vernier. By reasoning precisely 
similar to that above, it may be made very clear in every case, 
that the number of the coinciding vernier line is the same as 
the number of tenths of a millimeter in the remainder. If the 
student has difficulty in understanding the principle of the ver- 
nier, let him practice reading and reasoning as above, using a 
large model scale and vernier made of wood or of cardboard, 
the fixed scale divisions being each 1 cm. long and the vernier 
scale divisions being each .9 cm. (9 mm.) long. 

Note that the first line on the vernier is zero. 



MEASUREMENTS 9 

Data. — Tabulate the results. 

Zero Error. — Be sure to note the zero error (if 
there is one) when the jaws are placed together, and 
make the necessary correction for it. 

Part C 
BY SUBMERSION IN A GRADUATE 

Apparatus. — A graduated glass cylinder and some 
water are used. 

Operations. — The volume of the metal cylinder is 
to be determined by submerging it in the graduate 
and finding how many cubic centimeters of water 
it displaces. 

(a) Hold the graduate by the 
upper end between the thumb and 
forefinger, allowing it to swing 
freely, so that it hangs with the axis 
vertical. Fill it with water up to 
any convenient division mark ; and, 
holding it so that this mark shall +1 FlG ' 3 : ~ Sho ™& 

° t the position of the 

be on a level with the eye, read the eye when taking a 
position of the bottom of the curved rea mg ' 
surface, or meniscus, estimating to the tenth of a 
division. The single divisions may denote cubic 
centimeters in some graduates, or in others two cubic 
centimeters each. 

(J) Incline the graduate, and let the cylinder slide 
gently to the bottom. Carefully avoid splashing. 

(c) Take the new reading in the same manner as 
before. The difference of the two readings repre- 
sents the volume of the cylinder. 



-^ 



10 



LABORATORY EXERCISES IN PHYSICS 



Data. — Tabulate results as below: — 

Sources Of Er- Numehical Data 

ror. — Errors 
arise from (a) 
parallax, (6) 
personal equa- 
tion, (e) any 
lack of correct- 
ness of the 
scales. 

Note. — The error involved in reading from the bottom of 
the meniscus instead of from the middle is eliminated by sub- 
traction. It is easier to read accurately from the bottom. 

Additional Work. — If it is desired to do additional work, 
a cube or other regular solid may be measured as in Parts A 
and B. The volume of an irregular solid may be determined 
as in Part C. 

Lessons. — These are similar to those to be derived 
from Exercise 1. Let the student frame a concise 
and lucid statement of them. 



Trials 


1. (C.C.) 


2. (c.c.) 


1st reading 






2nd reading 






Volume 






Mean volume 







Exercise Number 3 

determination of mass by weighing 

References 

A 23-25, 92 GE 6 H & W 52, 57-58 



C 46-48, 98-100 
C & C 9, 10, 95 



GE6 
GP 3-6, 35 
H15 
W & H 11-14, 56, 62 



L 58 

S 18-23, 176 



Apparatus. — The apparatus consists of a balance 
and a set of masses, technically called " weights," a 



ME A S UBEMENTS 



11 



pair of pincers for handling the weights, and the 
solid used in Exercise 2. 

The Equal Arm Balance. Operations. — (a) See 
that the balance and the weights are free from dust. 

(6) See that all 
the weights are pres- 
ent. To ascertain 
this easily, notice 
whether the sockets 
in which the larger 
weights belong are 
all filled; then see 
that all of the smaller 
weights are in order 
in a tray provided 
for the purpose and 
placed near the cen- 
tre of the table, so 
that they will not be 
dropped upon the 
floor. The fractional 
denominations in 
most students' sets 
are as follows: deci- 
grams, 5, 2, 1, 1 ; centigrams, 5, 2, 2, 1. Report 
immediately if the set is incomplete or if the balance 
is not in perfect condition. 

(V) Adjust the balance to equilibrium by adding 
fine sand to the lighter pan till the pointer swings 
to equal distances on opposite sides of the zero posi- 
tion. If too much should be added, remove some. 




Fig. 4. — Showing a convenient 
method of supporting a " German hand 
balance." 



12 LABORATORY EXERCISES IN PHYSICS 

(d) Place the object near the centre of one pan 
and the weights on the other, the largest in the cen- 
tre and the others close around it. The weights 
should be tried in order, beginning with one known 
to be large enough. If the last weight be too great, 
replace it by the next smaller ; if too small, add the 
next smaller. In this manner, continue with the 
systematic trial of the weights until the opposite 
excursions of the pointer are equal. 

(e) Add up the weights in the pan. Their sum 
is equal to the mass of the object. 

(/) Add up the weights remaining and add their 
sum to the sum of those in the pan. Obviously, if 
the result is the total number of grams in the set, it 
is known that no mistake has been made in the count, 
and that no pieces have been lost. 

(#) Remove the object to the other pan and weigh 
as before. Take the mean of the two weights thus 
obtained and record it as the mass of the object. 

(K) When done with the weighing, see that both 
scales and weights are in perfect order, return the 
weights and pincers to their proper places. These 
directions are to be folloived in all subsequent weighings 
unless it be otherwise ordered. 

Precautions. — (a) The weights and scales must be 
kept free from dust and liquids. 

(J) The weights must be handled with pincers only. 

(c) The balances should not be permitted to vi- 
brate while object or weights are being placed in 
the pans. 

These directions apply to balances that have no 



MEASUREMENTS 13 

adjusting screw and no beam and pan arrests. If 
the balances are provided with beam and pan ar- 
rests, the levers that work these should be lifted each 
time before adding or removing object or weights, so 
as to prevent swinging during these operations. If 
there are no arrests, the pan may be held in the hand 
while the load is being changed. If there is a screw 
for adjusting to equilibrium, this is turned toward 
the lighter side, instead of adding sand. Hand bal- 
ances can be conveniently suspended upon a vertical 
support rod by means of a screw clamp. The pans 
should not be far above the surface of the table. 

The Trip Scales. Operations. — (a) Place the 
slider at zero. 

(5) See that the ends of the knife-edge do not rub 
against the ends of the bearings. If they do so, the 




Fig. 5. — The Trip Scales. 

beam will not oscillate freely, but will come to rest 
rather suddenly. Move the beam very slightly for- 
ward or backward till there is no friction. 

(<?) In front of the pointer are two little nuts. 
Turn the right-hand nut toward you, so that the two 



14 



LABORATOBY EXEBCISES IN PHYSICS 



nuts are unlocked ; then turn both nuts toward the 
lighter pan till the balance is adjusted. Lock the 
nuts in place by turning them toward each other. 

(d) Weigh as with the equal-arm balance to within 
5 grams ; then move the slider. 

(e) The scale reads grams and tenths up to 5 
grams ; this reading is to be added to the sum of the 
weights if they are on the right-hand pan, and sub- 
tracted if they are on the left. (Why ?) 

Data. — Tabulate the results as below. 
Sources of Error. 

-State What er- Numerical Data 

rors may arise 
from (a) parallax, 
(5) personal equa- 
tion, (c) friction, 
(tT) inaccuracy of 
weights, (e) in- 
equality of the 
arms of the bal- 
ance. (/) Which 
is eliminated by 
double weighing ? 
Lesson. — State 
in your own words what you have learned. This, 
the usual method of measuring mass, is based upon 
the principle that, at a given place, the mass of a 
body is strictly proportional to its weight. In 
Exercise 4 the student will learn that masses 
may be compared without reference to the earth's 
attraction. 



Substance 




Form 




Number 




Weight on right pan 


g- 


Weight on left pan 


g- 


Mean weight 


& 



ME A S UBEMENTS 



15 



Supplementary to Exercises 2 and 3 

DENSITY 
References 



A 155 


GE 6, 114 


L32 


C49 


GP 147, 148 


S177 


C & C 140, 141 


H 145 
H & W 59 


W & H 15 



Numerical Data 



Purpose. — The purpose of this exercise is to cal- 
culate the density of the regular solid of exercises 
2 and 3. 

Definition. — The density of a substance is its mass 
per unit volume. 

If D repre- 
sent the density 
of any body, M 
its mass in 
grams, and V 
its volume in 
cubic centime- 
ters, it follows 
from the defini- 
M 



tion that D = 



V 



Volume from Ex. 2, Part A 




Volume from Ex. 2, Part B 




Volume from Ex. 2, Part C 




Mean volume from Ex. 2 




Mass from Ex. 3 




Mean density 




Name of substance 





grams per cubic 
centimeter. 

Calculation. 
— From Exer- 
cises 2 and 3, take the data called for in the accom- 
panying tabular form, enter them, and calculate the 
density by dividing the mass by the volume. 



CHAPTER II 

mechanics of solids 

Exercise Number 4 

comparison of masses by the acceleration 

METHOD 

References 

A 27, 11, 60-66 GP 9-11, 29, 32-38, 41, 44, 63, 78 

C 2-7, 14, 16-21, 25-29, 33, 34, H 35-40, 44-46 

45, 50, 51, 54-56, 58, 63 H & W 62-65, 67 

C & C 30-34, 39-44 L 1-12, 29-36, 41-49 

GE 10-12, 22, 26, 27, 31-34 S 18-25, 175, 176 
W & H 16, 17, 161, 168, 174, 178-183 

Purpose. — The purpose of this exercise is to apply 
equal forces to two masses for equal time intervals, 
and to determine whether the greater or smaller mass 
acquires the greater velocity ; to determine whether 
their masses are equal if with forces equal they re- 
ceive equal accelerations ; and to learn what degree 
of accuracy is possible in adjusting masses to equality 
by this method. 

Apparatus. — The apparatus is as follows : Two 
cars, provided with hooks or screws at front and 
rear ; two rubber bands or strips of pure gum tubing, 
r, r v of equal lengths and elastic forces, and with 
loops at their ends ; two smooth boards, i?, B v with 

16 



MECHANICS OF SOLIDS 



hooks near their ends; a supply of 
lead weights or of iron nuts and 
nails; a spring balance, or a pair 
of trip scales and weights ; a small 
S-shaped hook of stiff wire. 

Operations. — (a) By means of 
the S-hook join the two bands and 
stretch them over a measuring stick, 
so that the ends of the bands are at 
the ends of the stick. If their 
elastic forces are equal when they 
are equally stretched, the junction 
will be at the middle of the rule. 
Why? If the S-hook does not lie 
exactly over the middle division, the 
stronger band must be trimmed 
along its edge until the hook remains 
in the right position. 

(K) Place a load of nails and nuts 
in one car, and of nails only in the 
other ; attach the rubber bands to 
the cars and to one of the pairs of 
hooks in the boards ; draw back the 
cars until the bands are stretched 
far enough to give the cars moderate 
velocities. Now secure the cars by 
a piece of twine, looped upon the 
two hooks in the backs of the cars 
and passed around the second pair 
of hooks in the boards. 

(jo) Adjust the cars so that their 




o 

B' 
orq 



_1 



18 LABORATORY EXERCISES IN PHYSICS 

front edges are in the same line and the bands 
equally stretched. 

(c?) Hold a rule between the cars and the two front 
hooks, and parallel with the line of the front edges of 
the cars, so that the car boxes, but not the wheels, 
will strike the rule about where the rubber bands 
cease to pull. 

(e) With shears or a sharp knife, cut the twine 
between the two rear hooks, in order to release both 
cars at the same instant. 

(/) Note which car has the greater mass as in- 
dicated by the velocity which the tension of the rub- 
ber band imparts to it, and, by repeated trials, adjust 
the masses till the cars have equal velocities, which 
will be when they start and arrive at the same in- 
stant. The adjustment should be made by adding, 
say, eight nails at a time to the car of lesser mass. 
When the addition of eight nails causes this car to 
arrive later than the other, remove as many as neces- 
sary of this last eight, — one or two at a time. 

(#) Test the accuracy of the adjustment by de- 
termining the least number of nails which must be 
added, first to one load and then to the other, in order 
to cause a clearly perceptible difference in the time of 
arrival. 

(Ji) When the adjustment is completed, determine 
the mass of each car and its load by the method of 
weighing, with the trip scales, or in a pail suspended 
on the hook of the spring balance, estimating the 
fractions of scale divisions in tenths. 

(i) If time permits, repeat with different masses. 



MECHANICS OF SOLIDS 



19 



Observations. — (a) When the forces are equal and 
the masses evidently unequal, which mass is given 
the greater velocity ? 

(5) What is the effect, upon the velocity, of in- 
creasing the mass ? 

(<?) What is the effect, upon the velocity, of in- 
creasing the force ? (This can be done by stretching 
the band farther.) 

Data. — Let m = mass of first car and load, m f the 
mass of the second car and load, R and R' the first 
and second readings of the balance, P the mass of 
the pail (to be subtracted from R and W to obtain 
m and m'), and n the least amount of additional 
matter (grams) required to cause an observable 
change in velocity. If a trip balance is used, the 
pail will not be needed, and then m and m' are 
obtained directly. The only quantities to be tab- 
ulated will be m, ra', and n. 

Numerical Data 



Trials 


R 


IV 


P 


R-P = m 


Rt-P = mf 


n 


1 














9 














3 















Calculate and record your per cent error. 
Theory. — Let v and v r be the velocities of the cars, 
t and ti the time intervals during which they travel, 



20 LABOBATORY EXERCISES IN PHYSICS 

and F and F f the forces applied; then F = — and 

it 
F f = — — . (Force is measured by the momentum it 

b 

can impart in unit time.) But F= F 1 (hypothesis), 
hence — = — — -. Also v = v r and t = t f (because 

the cars start and arrive at the same instants, and 
pass over equal distances). Therefore dividing both 

members by the common factor - or — (which is the 
acceleration) we have m = ml • 

Sources of Error. — Some of the most important 
errors result from — 

(a) Parallax and personal equation in reading 
the balances and observing the arrival of the cars. 

(J) Inequality of the forces. The bands should 
be tested frequently and readjusted if necessary. 

(c) Difference in friction of the two cars. This 
difference, if it exists, can be eliminated by slightly 
tilting the boards by means of wedges until each car 
when started will move down its incline with uniform 
speed. 

Inferences. — (a) Do your observations and results 
confirm the deductions of the theoretical discussion 
above ? 

(5) Make a general statement of what has been 
deduced and verified. 

(c) Explain briefly how you would use this method 
to measure out a pound mass of sugar or coffee at a 
place where you could not make use of the weight 
method. 



MECHAXICS OF SOLIDS 21 

Notes. — If long rubber bands or tubing are not available, 
rubber bands may be linked together in threes or fours. If 
they are not long enough to give the cars a long run without 
stretching too far, the bands may be pieced' out with equal 
lengths of twine. During preliminary trials the cars may be 
held by a rule placed across their fronts, and may be released 
by raising the rule vertically without changing its direction. 
The weights supplied with the trip scales may be used instead 
of nails in one of the cars. In the discussion of this experiment, 
carefully avoid the use of the word " weight" except when referring to 
gravitation attraction. You are experimenting with masses exclu- 
sively except in the final test by weighing. (How is the weight 
effect eliminated ?) 

Exercise Number 5 
concurrent forces 

References 

A 67-72 GE 41-44, 54-56 H & W 82-83 

C 57, 63 GP 12-45, 56-58 L 25, 96-106 

C & C 45-47 H 47-49 W & H 41-46, 184 

Purpose. — The purpose of this experiment is to 
verify the principle of parallelogram of forces ; that 
is, to compound sets of forces in accordance with this 
principle, and find whether the force thus determined 
is the true resultant. 

Apparatus. — The arrangement is shown in the 
diagram. Three spring balances are used, to meas- 
ure the forces exerted by the cords and lengths of 
plumber's safety chain. The chains are joined to 
each other and to the balances by small key rings or 
harness rings so that they lie perfectly flat ; and the 




Fig. 7. — Apparatus arranged for experimenting with concurrent forces 



MECHANICS OF SOLIDS 23 

cords are secured at any desired points at the edges 
of the table by clamp hooks provided with thumb 
nuts. 

Operations. — (a) Let each of three students pull 
steadily on a balance and secure it to a clamp hook. 
Let the pulls be made at random, in any convenient 
directions and with any convenient forces, but so that 
equilibrium shall result. 

(6) A note-book page is to be slipped under the 
chains by a fourth student, who, when the equilib- 
rium is secured, marks on the page the positions of 
the chains. This he does by thrusting a pin through 
the links, exactly in the middle line of the chain, and 
pricking two points 1 1, 2 2, 3 3, for each line. The 
points should be as far apart as possible. Each line 
is to be marked with a letter, which will represent the 
force in the tabular form. 

(#) At the same time the other three students 
record the readings of their respective balances. 

(cT) The positions of the corresponding lines of 
direction being fixed, and the lines drawn meeting at 
a point, record the magnitudes of the forces on their 
respective lines, remembering to add the proper zero 
correction for each balance. 

(e) Let each student in turn get at least one such 
set of lines in his note-book; and using these lines, 
construct the parallelogram of the forces so recorded. 

Employing any convenient scale, cut off each line 
proportional in length to the magnitude of the force 
it is to represent. 

Taking any two of these lines as adjacent sides, 



24 LABORATORY EXERCISES IN PHYSICS 

complete a parallelogram, and draw the diagonal 
from the meeting point of the three lines (point of 
application) to the opposite vertex. The chosen 
scale must be small enough so that the whole diagram 
will go on the page. 

(/) Measure this diagonal to find the numerical 
value of the resultant force, record its value, and 
compare it, both as to direction and as to magnitude, 
with that of the third of the three forces (the equil- 
ibrant). 

Zero Correction. — When used horizontally, a spring 
balance graduated to be used in a vertical position 
gives a small negative reading under no load. 
(Why ?) This is called the zero error and its 
amount must be obtained as follows : Hold the 
balance in the vertical position, and slowly change 
it to the horizontal, lightly tapping ;t the while. 
(Why?) 

Take off on a pair of dividers, or a straight-edged 
bit of paper, the length of the zero error ; and apply 
it to the scale of the balance so as to measure its 
amount in scale units and tenths. Since all horizontal 
readings of the balance will be smaller than they 
ought to be by just this amount, each reading must 
be corrected by adding to it the amount of the zero 
error. The readings thus corrected give the real 
values of the forces observed. 

Data. — Record (a) the scale of the diagram ; 
(5) the values of all four forces (corrected balance 
readings in pounds and tenths, or in grams); 
(<?) lengths of all four lines which represent the 



MECHANICS OF SOLIDS 



25 



forces ; (c?) name the lines representing both compo- 
nents, the resultant and the equilibrant, and show 
their directions by arrow tips; (e) record the amount 
and per cent of the experimental error, i.e. the differ- 
ence between the numerical values of the equilibrant 
and of the resultant. 

Place the data near the diagram in tabular form, 
as below. 



Scale of the Diagram . . . . 
Numerical Data 



Name of Force 


Force 

(Letters) 


Balance 
Beading 


Zero 
Correction 


Force 

Amount 

IN LBS. or g. 


Length 
of Line 


Component 












Component 












Equilibrant 












Resultant 












Experimental 
error 




Per cent error 





Sources of Error. — Errors may arise from (a) 
parallax ; (J) friction of the balances, chains, or 
cords; (<?) inaccuracies in construction and meas- 
urement. Friction may be avoided by lightly tap- 



26 LABORATORY EXERCISE IN PHYSICS 

ping the balances and cords to allow them to come 
into position in straight lines. 

In constructing the parallelogram, see that the 
pencil is kept sharp and the dividers in good condi- 
tion. Use the utmost care. If all the work is care- 
fully done, the per cent of error will be small. To 
compute the per cent of error, multiply the error by 
100 and divide by the value of the equilibrant, which 
may be taken as the base. A given error will be less 
important in proportion as the base is large. Hence 
use forces as large as practicable. 

Inferences. — Answer, in concise sentences, the fol- 
lowing questions: (a) Neglecting the experimental 
error, how does the resultant, as found in the experi- 
ment, compare in magnitude with the equilibrant ? 

(5) What is the direction of the resultant with 
reference to that of the equilibrant? 

(<?) Do you, therefore, conclude that the quantity 
determined in your experiment, and recorded as the 
resultant of the two forces that were chosen as com- 
ponents, is the true value of their resultant ? Copy 
and memorize the Principle of the Parallelogram of 
Forces as stated below. 

Principle Verified. — If two forces, acting at an 
angle upon the same point, be represented in direc- 
tion and magnitude by two lines drawn to any given 
scale, then the resultant of these two forces will be 
completely represented, on the same scale, by the 
concurrent diagonal of the parallelogram constructed 
upon those two lines as adjacent sides. 

In bridges, frames of buildings, and machinery, the 



MECHANICS OF SOLIDS 27 

composition and resolution of forces have count- 
less applications. Engineers calculate these forces 
accurately, so as to use materials sufficiently strong, 
and yet avoid excessive amounts and the consequent 
weight and expense. Pick out resultants, compo- 
nents, and equilibrants in structures, machinery, sail- 
boats, kites, etc. Look for tensions and pressures 
caused by weights and tenacities of parts, winds, 
" snow-loads," " struts," " ties," etc. 

Exercise Number 6 
parallel forces and the law op moments 

References 

A 69, 128-132, 134, 135 H 96-105 

C 60, 63, 74-77 H & W 84, 85, 99 

C & C 47, 93-97 L 53, 107-109, 113-117, 127, 137 

GE 45-49, 81-83 S 164 

GP 19, 46-49, 84-85 W & H 49-54 

Purpose. — In this exercise it is proposed (a) to 
investigate the laws of equilibrium for three parallel 
forces, and (6) to formulate a rule for determining 
the point of application, direction, and magnitude of 
the resultant of any given pair of parallel forces. 

Apparatus. — AB is half a meter stick, with wire 
nails driven through it at regular intervals along its 
axis, at right angles to its faces, and projecting about 
a half centimeter above and below ; c,c,c are pieces 
of stiff wire, bent into the form of clevises. Three 
spring balances, with cords and clamp hooks, are used 
to measure the forces, F v F v F s , in a manner similar 



28 



LABORATORY EXERCISES IN PHYSICS 



to that of Exercise 5. The bar is suspended by a 
wire, as shown, so that it hangs horizontally about a 

centimeter above the table. 
Operations. — (a) Arrange 
the balances so as to exert 
parallel forces as indicated 
in the diagram. At least 
four cases are to be made, 
by varying the relative dis- 
tances between the point of 
application, p v of the mid- 
dle .force and the points 
of application, p 1 and p s , of 
the two end forces. These 
distances are varied by 
placing the clevises over 
bar and moving the clamp 




Fig. 8. — Showing how the 
forces are applied to the sus- 
pended bar. 



different nails on the 

hooks along the ends of the tables. 

The forces may be varied in amount by drawing 
the cords forward or backward at the clamps and 
securing them by the thumb nuts when the desired 
tension is attained. 

(b) Choose any convenient ratios for the distances 
PiP 2 and p 2 p& e.g. Case I, ^; Case II, J; Case III, 



i or 



3 > 



Case IV, I or f . 



(c) Use the utmost care to avoid friction in the bal- 
ances or cords, to have the forces act all parallel and 
in the same plane, and to see that the bar is in a hori- 
zontal position just clear of the table. Be sure that 
the plane of the wire that supports the weight of the 
bar is exactly vertical. 



MECHANICS OF SOLIDS 



29 



Data. — (a) For each case make a diagram. Rep- 
resent distances and forces each on a scale appropriate 
to the size of the page, e.g. for distances, 1 cm. = 
5 cm. ; for forces, 1 cm. = 2 lbs., or 1 cm. = 100 g. 
Do not crowd more than two cases on a page. 

(5) Above each diagram state the scale to which 
it is drawn. 

(6) Underneath each diagram state what point is 
adopted as the centre of moments ; choose a different 
point for each case, but be sure to use that point only 
throughout that case. 

(cT) On the line representing each force, record its 
value in pounds and tenths, or in grams (corrected 
for zero error) ; also indicate its direction by an arrow 
point. 

(e) Near the line representing each arm, record its 
length in centimeters. 

Numerical Data 



Force 
(Letter) 


Balance 
Eeading- 


Zero 
Correction 


Force 
(Amofnt) 


Arm 


Moment 


F, 












F, 












F 3 












Sum 




Sum 





(/) For each case fill out a tabular form as above. 
Be careful to give the dimensions of forces and arms 



30 LABORATORY EXERCISES IN PHYSICS 

(lbs., g., or cm.) and the + or — signs of the forces, 
of the moments, and of the sums. If a force in one 
direction is called positive, one in the opposite direc- 
tion is negative ; and if a moment acting clockwise 
is called positive, one acting counter-clockwise is 
negative. 

The sums are understood to be the algebraic sums. 

Calculations. — Moment = force x arm. If the arm 
of any force = (i.e. if the centre of moments is iden- 
tical with the point of application of the force), the 
moment becomes 0. It should, however, be set down 
in its proper place. In solving the equation, form 
the habit of considering the moment of each force in 
turn from the left to right, not omitting any. 

Sources of Error. — State briefly the sources of 
error pertaining to the different parts of the appara- 
tus, and the operations and measurements, also the 
precautions necessary in order to minimize them. 

Inferences. — Frame a concise statement in answer 
to each of the following questions : (a) In order that 
three parallel forces in the same plane may be in 
equilibrium, what must be the numerical value of the 
algebraic sum of the forces, and also of the algebraic 
sum of the moments about any chosen point ? 

(5) If your results show small + or — quantities 
for the sums of the forces or of the moments, do you 
think they may fairly be regarded as due to experi- 
mental errors ? Why ? 

(c) Which of the conditions mentioned in (a) must 
be satisfied in order to prevent translatory motion ? 
and which to prevent rotary motion ? 



MECHANICS OF SOLIDS 31 

(cT) In each case, which force is the equilibrant of 
the other two, and how must their resultant compare 
with it in point of application, direction, and magni- 
tude ? 

(0) What, then, is the direction, and what the 
magnitude of the resultant of any two parallel forces, 
compared with those of the forces ? 

(/) How does the point of application of the re- 
sultant divide the line joining those of the two 
forces ? 

Additional Work. — If there is time for extra work, the stu- 
dents may experiment with fonr or more forces in the same 
manner as above, or repeat the experiment with the bar not 
perpendicular to the lines of direction of the forces. In the 
latter case they should remember to measure the arm of each 
force on a line perpendicular to its line of direction. 



Exercise Number 7 
centre of mass 





References 




A 94-95 


GE 50-53 


L 119, 120 


C 92-97 


GP 52-54 


S 161, 162 


C & C 52, 54-56 


H 74, 75 


W & H 57, 58 



Purpose. — The purpose of this exercise is to locate 
the centre of a mass of a pasteboard triangle, and to 
determine its relation to the medians. 

Apparatus. — The apparatus consists of the paste- 
board triangle, a pin, and a plumb-line, which may 
be a heavy button suspended by a thread. 



32 LABOBATOBT EXERCISES IN PHYSICS 

Operations. — (a) Pass the pin through the triangle, 
as near as possible to one vertex, and work it around 
in the hole till the triangle can oscillate freely 
about it. 

(6) Tie the plumb-line to the pin, and drive the 
latter into the wall. Adjust the thread till it is 
very near the triangle, but not touching it. 

(e) Tap the triangle lightly, so that it will oscil- 
late and then come to rest. 

(c?) By means of two fine pencil-marks locate on 
the triangle the position of the vertical line through 
the point of suspension, as indicated by the plumb- 
line. 

(e) Repeat the operations for the other two ver- 
tices of the triangle. 

(/) Draw the lines on the triangle. If the work 
has been accurately done, they will meet in a point. 

(<7) Test the accuracy of your work by observing 
whether you can balance the triangle upon a pin- 
point at the intersection. 

(K) Measure and record the distances from the 
points in which the lines intersect the sides of the 
triangle to the adjacent vertices. 

Data. — (a) Choosing a convenient scale, draw a 
diagram of the triangle, together with the lines 
mentioned in Operations (d) to (/). 

(6) Record, either in tabular form or upon the 
diagram itself, the measurements of Operation (K). 

(e) Record the scale of the diagram. 

Sources of Error. — Make a concise statement, 
pointing out the sources of error. 



MECHANICS OF SOLIDS 33 

Inferences. — Answer in brief, complete sentences, 
the following questions : — 

(a) Does each of the lines drawn in Operation (/) 
contain the centre of mass ? Why ? 

(5) How is the point determined ? Why ? 

(<?) Are the lines medians of the triangle ? Why ? 

(cT) What is the relation of the centre of mass to 
the centre of figure ? 

(0) Would this be true if the triangle were not 
of uniform density and thickness ? 

(/) Where is the centre of mass with reference 
to the thickness of the triangle ? 

Additional Work. — If there is time for additional work, 
a good illustration of the practical value of this principle is 
to cut out to scale a pasteboard model of half a stone bridge 
arch, and by determining the centre of gravity of the model, 
locate the centre of gravity of the semi-arch. 

Note. — This exercise may profitably be performed by the 
students at their homes. 



Exercise Number 8 
weight of a bar. law of moments 

References 

A 69, 128-132 GE 47, 48, 50, 52, 81 H & W 99 

C 60, 63, 74-77, 93-94 GP 49, 52-54 L 120, 127, 137 

C & C 55, 93, 94 H 51, 96-105 W & H 59 

Purpose. — The purpose of this exercise is to apply 
weights to a wooden bar, and by calculating their 
moments about a chosen point, determine the weight 



34 



LABORATORY EXERCISES IN PHYSICS 



i i i i i 

/ i i i » i i i 




w -*- w. 



^ 



1 I I 



of the bar, which is to be the unknown quantity in the 
equation of moments. (Afterward, the accuracy of 
the method is to be tested by weighing the bar and 
comparing the two values thus obtained.) 

Apparatus. — (a) The bar ah is purposely made 
of irregular shape by fastening to its end a block, 

or a strap of sheet 
lead. 

(5) Sliding sup- 
ports with project- 
ing knife-edges, and 
a block with bear- 
ings, for a fulcrum, 
are provided ; but 
if desired the bar 
may be suspended 
by a slip noose of 
thread, as shown, 
instead of using the support and bearings. 

(V) Pieces of metal are to be used to exert forces. 
(d) A balance and weights, or a spring balance, is 
used for weighing. 

Operations. — (&) Place the bar in the sliding sup- 
port, which it should fit snugly, and rest the knife- 
edges of the latter upon their bearings. Move the 
bar through the support (or thread loop) until it will 
remain in equilibrium and horizontal. Two forces 
only are now acting on the bar, — its weight, W, a 
downward force, and the resultant supporting press- 
ure of the bearings (or loop), an upward force. 
These two forces are in equilibrium ; and their com- 



v w < 



Fig. 9. — Showing how the forces act on 
the bar. 



MECHANICS OF SOLIDS 35 

mon point of application is the centre of gravity, (r, 
of the bar, i.e. the centre of gravity of the bar is now 
a little below the line of the knife-edges (or in the 
vertical plane of the loop of thread). 

(5) Measure accurately the distance from one end, 

a, of the bar, to Gr. 

(e) Ascertain the weight, W v of one of the pieces 
of metal, and hang it at a. Now balance the bar as 
before. There are, this time, three forces : W, ap- 
plied at 6r, W x applied at a, and the upward pressure 
of the bearings (equal to W+ W{) applied at the 
observed point, which we call c. 

(cT) Measure aGc and ac. 

(e) Diagram the bar and applied forces, with their 
arms, and near the lines representing these quantities 
record their values in grams and centimeters. Give 
directions of forces by arrow tips. 

CO Write the equation of moments with respect 
to point a. 

(#) Make a second case of equilibrium with an 
additional weight, W v suspended at or near the end, 

b. Now there are four forces. (What are they, and 
what is the amount of the upward pressure of the 
fulcrum ?) Diagram, record forces, leverages with 
respect to a, and directions as in the previous cases, 
and again write the equation of moments. 

(K) In each of the equations of moments thus 
written, W is the only unknown quantity. 

Solve each equation for TT, and average the result- 
ing values. This is the mean value of the weight of 
the bar as deduced from the data of the experiment. 



36 LABORATOBY EXEBCISES IN PHYSICS 

(i) Now weigh the bar and compare the value of 
W thus obtained with the average of the values cal- 
culated by applying the principle of moments. 

(&) If time permits, make up other cases for your- 
self, and thus become satisfied that the weight of the 
bar is one of the forces to be reckoned with in every case 
of equilibrium of the bar. 

Data. — (a) Under the diagram for each case, set 
forth the numerical data in a neat tabular form 
similar to that of Exercise 6. 

There will be no zero correction, so that two of the 
columns are not needed. 

(J) At the end of the record tabulate all the calcu- 
lated values of W and their average, together with the 
value of W obtained by weighing, the difference between 
the mean calculated value and the value by weighing 
(i.e. the error), and the percentage error (i.e. what 
per cent of the weight "FT this difference is). 

Sources of Error. — State them. The most serious 
ones are likely to occur through inaccuracies in meas- 
uring the distances on the bar, and as a result of 
friction at the bearings. 

Inferences. — Make concise statements in answer 
to the following questions : (a) Can the weight of a 
body be considered as the resultant of a set of parallel 
forces ? What forces ? 

(J) What name is given to the point of application 
of this resultant ? 

(c) Is the weight of a beam, rafter, bridge truss, or 
other piece of structural work a force that should be 
taken into account in calculating the stress upon it ? 



MECHANICS OF SOLIDS 37 

Additional Work. — The problem may be repeated with the 
weight of the bar as a known quantity (determined by weighing) 
and the distance of the centre of mass from a as the unknown, 
thus locating the centre of mass by calculation ; or the weight 
and this last distance may be determined and the weight W x 
calculated. In each case compare the calculated value of the 
unknown quantity with the measured value. Look for moments 
of forces in structures and machinery. 



Exercise Number 9 
work. inclined plane 

References 

A 80, 121-127, 140, 141 H 53, 60-62, 94, 111 

C 64-66, 69, 71-73, 78 H & W 87, 97, 102 

C & C 48, 89-92, 101-103 L 77-80, 93, 137 

GE 67, 71-73, 77, 78, 83 S 143-145, 159, 160 

GP 62, 70, 74-76, 80, 86 W & H 46, 199-203, 206 

Purpose. — The purpose of this exercise is to 
determine the relation between the amount of work 
done in moving a body upward along an inclined 
plane and that done by lifting it vertically through 
the same difference of level. 

Apparatus. — A car, and some iron nuts or other 
weights, and an inclined plane, are placed as shown. 
A spring balance is attached to the car by a short 
stout cord or chain. A metric rule and a pail (or a 
basket) are also provided. 

Operations and Data. — Holding the balance parallel 
to the plane, and keeping the line of sight perpen- 
dicular to the plane of the scale at the point of 




38 LABORATORY EXERCISES IN PHYSICS 

reading, move the car up and down the plane, and 

read the amount of 
the force indicated 
while a uniform velo- 
city is maintained. 
With the usual pre- 
cautions, take the 
measurements of the 
quantities indicated 

Fig. 10. — Showing how the force is below : 

applied and observed. _ . 

A, the height ot 
the plane from floor to the point vertically above 
the table edge. 

Z, the length of the plane from floor to the same 
point. 

z, the zero correction for the balance in position. 

u, force required to maintain uniform velocity up 
the plane. 

d, force required to maintain uniform velocity 
down the plane. 

/, ( = — ^ — ), the mean force required to balance 

the component of weight of car and load along the plane. 

.F, ( = / — 2), the mean force as above, corrected 
for zero error. 

W + p, the combined weight of the car and its 
load along with that of the pail in which it is to 
be weighed. 

p, the weight of the pail. 

W, (= [TT + p~\ — £>), the combined weight of car 
and load. 



MECHANICS OF SOLIDS 



39 



F xl, the work done along the displacement, I, by 
the force, F. 

Wxh, the work done in moving the mass against 
the resistance, W, through the vertical displace- 
ment, h. 

e, the experimental error. 

The values of h and I are to be taken in inches 
to the nearest |-th, and reduced to feet and hundredths ; 
balance readings in pounds and tenths. Or if forces 
are recorded in 
grams, the dis- 
tances must be 
in centimeters ; 
and if forces are 
recorded in kilo- 
grams, the dis- 
tances must be 
in meters. The 
amounts of work 
will then be in 
foot-pounds, or 
gram - centime- 
ters, or kilogram- 
meters respec- 
tively. Tabulate 
as here : — 

Calculations. — The amount of error is the numerical 
difference between F xl and Wxh. The percentage 
error is calculated by finding what per cent this 
difference is of the mean value of the two amounts 
of work. 



u 




Numerical Data 


d 




Exercise 9 


f 




W-p 




z 




P 




F 




W 




I 




h 




Fxl 




Wxh 




e 




% error 





40 LAB ORATORY EXERCISES IN PHYSICS 

Sources of Error. — State the sources of the errors 
pertaining to (a) the length measurements, (6) the 
balance readings, (<?) the positions of the balances 
and cord in moving along the incline. 

Inferences. — (a) Judging by your observations 
and the experience of the others in the class, do you 
think it fair to infer that the difference between the 
corresponding values of W x h and F x I are wholly 
due to experimental errors ? (Why ?) 

(6) Make a complete and general but concise state- 
ment of the relation existing between the quantities 
compared. 

Exercise Number 10 

WORK. INCLINED PLANE (continued) 

Keferences 

A 141 C&C 101-103 Hill 

C 71-73, 78 GP 74-76, 80-86 S 159, 160 

Purpose. — The purpose of this exercise is to de- 
termine the relation between the amount of work 
done in moving a body upward along an inclined 
plane by means of a force applied parallel to the base 
of the plane, and the amount done in lifting the same 
body vertically through the same difference of level. 

Apparatus. — This is the same as that used in the 
preceding exercise, with the addition of the yoke y, 
which is attached to the front of the car, as shown. 

Operations. — Adopt the same mode of procedure 
as in Exercise 9, except that the balance and cord 
are to be kept always horizontal. 



MECHANICS OF SOLIDS 41 

Great care and some practice will be required in 
order to do this successfully. A long stout cord 
attached to the ring of the balance will aid greatly 
in applying the pull. Let one person pull the cord, 
while the second steadies the balance as it moves, 
and a third takes the readings. 




Fig. 11. — Showing how the force is applied parallel to the base of 
the plane. 

Instead of the length of the plane, the base is 
measured from where the inclined plane intersects 
the plane of the floor to the point where a plumb- 
line from the table edge meets the floor. 

Data. — Tabulate the results precisely as in the pre- 
ceding exercise, excepting that b (base), P (force 
parallel to base), and P x b are recorded in place of 
Z, F, and F x I respectively. 

Sources of Error. — These are similar to the fore- 
going. Note that the zero correction is to be deter- 
mined with the balance in the horizontal instead of 
the inclined position. 



42 LABORATORY EXERCISES IN PHYSICS 

Inferences. — (a) Make a complete and general, 
but concise, statement of the relation investigated. 

(b) Judging from your own observations and those 
of your classmates in this and the preceding exercise, 
do you infer that the amount of work done in lifting 
a weight through a given difference of level is dependent 
or independent of the length of the path ? 

(<?) If the path is longer, what about the amount 
of the force required to do the work ? 

Can this relation be stated mathematically? If 
so, write the proper expression. 

Additional Work. — If it is desired to assign additional work, 
let new sets of measurements be made, using different inclina- 
tions of the plane, and let it be determined whether the propor- 
tions — = - and — = - always hold true. Note that these 
W I W b 

proportions may be written F x I = W x h and P x b=W x h. 
Find examples of work wherever you see bodies moving. 

Exercise Number 11 
laws of the pendulum 

References 

A 106, 112-120 GE 60-63 H & W 74-81 

C 68, 87-89 GP 65-69 L 73, 141-143 

C & C 68-77 H 83-91 S 173, 174 

W & H 189-193 

Part A 
EFFECT OF LENGTH AND AMPLITUDE 

Purpose. — The purpose of Part A is twofold: 
(a) to learn whether the period of a pendulum is 




MECHANICS OF SOLIDS 43 

affected by the amplitude of vibration, and (5) to 
determine whether the period of a given pendulum 
varies directly as the square root of its length. More 
briefly, the aim is to verify the laws of the pendulum 
regarding amplitude and length. 

Apparatus. — (a) The pendulum is made of a bullet 
of about 1.5 cm. diameter, into which is moulded a 
very small wire loop. A silk thread 120 cm. long 
is attached to this loop at one 
end, and passed into a knife slit 
in a cork near the other end. 

(J) By means of a screw 
clamp attached to a vertical rod, 
the cork is firmly supported so 
that the thread hangs perpen- 
dicular to the face from which 

it emerges. Fig. 12.— Showing how the 

" k n pendulum is suspended. 

(<?) The meter stick and rect- 
angular block of Exercise 1 and the calipers of Exer- 
cise 2 are needed for measuring the lengths and the 
diameter of the bob. 

(d) For the time measurements a good timepiece, 
capable of marking seconds, is needed (e.g. a student's 
watch, a stop-watch, a metronome, or, best of all, a 
telegraph sounder, electrically connected with a good 
laboratory clock. 

Operations. — (a) Carefully measure the diameter 
of the bob. 

(5) Loosen the thumb-nut of the clamp, and draw 
the thread up or down through the slit in the cork, so 
as to make the pendulum between 25 and 50 cm. long. 



44 LABORATORY EXERCISES IN PHYSICS 

(<?) Tighten the nut (if necessary, give the end of 
the thread several turns around the cork, passing 
it again into the slit), so that the thread will not 
slip. 

(d) Measure the length of the pendulum as fol- 
lows : place the end of the meter stick against the 
under surface of the cork, and so that the thread 
hangs vertically just in front of the scale. Now, 
holding the block against the scale with its upper 
surface horizontal and below the bob, slip it upward 
carefully till it is just tangent to the bottom of the 
bob, and read on the scale the distance of this sur- 
face from the end of the rule. This is the distance 
from the bottom of the cork to the bottom of the 
bob; and the approximate real length of the pen- 
dulum is obtained by subtracting from it the radius 
of the bob. (Why?) 

(e) Record the data in centimeters and hundredths. 
(/) In order to adjust the rule as above, it may be 

necessary to slide the clamp to the top of the sup- 
port, or even to remove it altogether ; but after the 
length is measured it should be readjusted on the 
rod at such a height that the bob hangs about 2 cm. 
above the surface of the table. This is the most 
convenient position for the work that follows. 

(#) Set the pendulum swinging over a small arc 
not exceeding 10° of a circumference. Let the 
length of the arc be roughly determined by a meter 
stick placed beneath the bob. 

Qi) Place your pencil point near the top of a sheet 
of paper, but not touching it, and move the pencil 



MECHANICS OF SOLIDS 45 

back and forth in unison with, the pendulum, keeping 
the bob always in sight. 

(i) At the instant when the second hand of the 
timepiece reaches zero, lower the pencil point so that 
it touches the paper, and continue the motion in 
unison with the pendulum, at the same time slowly 
moving the hand toward the bottom of the sheet, 
thus making a zigzag line on the paper. Each seg- 
ment of this broken line represents a single oscilla- 
tion of the pendulum, and any fraction of a segment 
represents approximately a corresponding fraction of 
an oscillation. 

(y) At the instant when a given number of sec- 
onds is completed (say 60 or 100) raise the pencil 
from the paper. 

(Jc) Count the number of segments and tenths of 
a segment in the zigzag record line. The result is 
the number of oscillations made by the pendulum 
during the given number of seconds. 

(J) It is better to let another student work with 
you (unless the stop-watch is used). He should say 
"tick" at the beginning of the time interval agreed 
upon, and then count (in silence) "one, two," etc., 
up to (say) fifty-nine (this time aloud) ; at the 
sixtieth click of the sounder he again says u tick." 
If the second's dial can be seen, it should always be 
watched in order to verify the count. If the stop- 
watch is used, the student can work better alone, 
counting one hundred oscillations of the pendulum, 
the watch being started at the beginning of the 
interval and stopped at the end of it. In this case, 



46 LABORATORY EXERCISES IN PHYSICS 

place a pointer in front of the thread near the bob 
at its lowest position, and reckoning the time between 
two successive passages of the pointer in the same 
direction as the time of two oscillations. Instead of a 
stop-watch an ordinary watch may be used. Set the 
minute and second hands so that they begin the 
minutes together. Estimate fifths of a second. 

(m) Without altering its length, vibrate the pen- 
dulum over a different arc (less than 15°) and deter- 
mine as before the number of oscillations in a given 
time. 

(n) Repeat for a third length of arc (still, less 
than 15°). 

(0) Adjust the pendulum to a length between 50 
and 75 cm.; determine the real length, and make 
observations for three different short arcs as before. 

(p) Make the length from 75 to 100 cm., and 
repeat all the operations as above. 

Data and Calculations. — Tabulate the results as 
below. Let D be the distance from cork to bottom 
of bob, It the semi-diameter of the bob, I the real 
length (equal to D — iT), a the length of the arc in 
centimeters, o the whole number of oscillations in 
the given time, s the number of seconds required to 
make the number of oscillations 0, t the period, or 
time of one oscillation (equal to the number of times 
is contained in s), and h the ratio of the period 
to the square root of the corresponding length (i.e. 

— - ) for each determination of t. k is to be expressed 
as a decimal fraction. 



MECHANICS OF SOLIDS 



47 



Numekical Data 





Length of 

Aec 

a 


Oscilla- 
tions 




Number of 

Seconds 


Period 
t 


Eat 10 


D 












R 












I 












D 












R 












I 












D 












R 












I 













Sources of Error. — State concisely what errors may 
pertain to (a) the timepiece, (5) the observers, 
(c) the measurements of length. 

Inferences. — In complete sentences, answer the 
questions below. 

(a) Do your values of t corresponding to a given 
length, differ by amounts too great to be ascribed to 
the inevitable errors of the experiment ? 

(V) If not, when the length and place remain the 



48 LABORATORY EXERCISES IN PHYSICS 

same, is the period dependent upon the length of the 
arc.* 

(V) Do you consider it fair to assume that the 

values of — are all equal, or, in other words, that 

* Vz 



VI 



is a constant ratio for all lengths ? 



(ci) If I and V be two lengths, and t and t r be the 
corresponding periods, and if — = k (a constant 

t! ^ t VZ 

quantity), and — = Jc also, show that — = . 

(e) If you have answered (5) and (e) in the affirm- 
ative, state the two laws of the pendulum which 
you have verified by your experiments as far as they 
go. 

Part B 

ACCELERATION OF GRAVITY 

Purpose. — The purpose of Part B is to calculate 
the mean value of g at the school laboratory from the 
data obtained in Part A. 

Calculations. — (a) Put the equation of the pendu- 
lum, t = 7r\/-, into the form g=^-- 
^g t 2 

(6) In this formula, substitute 3.1416 for 7r. Sub- 
stitute for I the first value of length taken from the 
tabulated results of Part A. Average the values of 
the period of oscillation belonging to this length, and 

* Half the arc measures the amplitude of the oscillation, and 
theoretically it should not exceed 5°, but practically it will be diffi- 
cult in this experiment to make it quite so small. 



MECHANICS OF SOLIDS 49 

put the resulting quantity in place of t. Solve the 
equation for g. 

(c) In like manner, substitute and calculate the 
value of g from each of the other lengths and its 
corresponding mean period. 

(d) Tabulate and average these values of g to find 
the mean acceleration of gravity at your laboratory. 

(#) If given the theoretical value of g in your lati- 
tude by your teacher, find your error by subtraction, 
and calculate your percentage error. To do this, 
multiply your error by 100 and divide by the given 
value of g. 

Part C 

GRAPHIC REPRESENTATION OF THE LAW OF LENGTH 
AND PERIOD 

Purpose. — The purpose is to plot a curve, showing 
the relation between the lengths of a pendulum and 
the corresponding periods of oscillation. 

Operations. — (a) Near the lower left-hand corner 
of your note-book page, which is ruled in ^ cm. 
squares, or on engineer's cross-section paper, choose 
for the origin a point, (2, at the intersection of any 
two lines. 

(5) From draw a vertical line, say 10 cm. long, 
and mark it, Axis of Ordinates. From draw a hori- 
zontal line of the same length and mark it, Axis of 
Abscissas. 

(c?) Near the axis of abscissas, write, " Values of I. 
Scale ; 1 cm. = 10 cm.," and, using this scale, mark 



50 LABORATORY EXERCISES IN PHYSICS 

points on the axis of abscissas at distances from 
equal respectively to the values of I that were used 
in your experiments. Opposite each of these points 
place its numerical value (I in cm.) and the number 
of scale units corresponding. 

(cT) Near the axis of ordinates, write, " Values of 
t. Scale; 1 cm. = .1 second," and, using this scale, 
mark points on the axis of ordinates at distances 
from equal respectively to the values of t obtained 
in your experiments. Opposite each of these points 
place its numerical value in seconds and tenths, and 
also in terms of the scale. 

(e) From the point belonging to the smallest value 
of Z, erect a dotted line parallel with the axis of ordi- 
nates ; and from the point belonging to the corre- 
sponding value of £, draw a dotted line parallel to the 
axis of abscissas. Produce these two lines till they 
meet in a point. This point is, theoretically, a point 
in the required curve ; and the two dotted lines are 
its coordinates, — the vertical being its ordinate and 
the horizontal being its abscissa. 

(/) Draw the abscissa and ordinate of the point 
which represents the next value of I and its corre- 
sponding value of £, and mark the second point as 
you marked the first. Continue the process until all 
the values of I and their corresponding values of t 
have been plotted and the intersections of their 
coordinates marked. It is well to draw a little 
circle round each point. 

(#) Now sketch lightly a smooth curve through 
the origin and through the points determined. If it 



MECHANICS OF SOLIDS 51 

cannot be made to pass through all the points with- 
out sharp bends or turns out of its course, make it 
follow an average course, taking in the largest num- 
ber of points that it can be made to pass through 
without sharp bends. 

(A) Line in the curve, preferably with red ink, 
making it of uniform thickness. In drawing the 
curve, a piece of whalebone or a " French curve " will 
be of assistance. 

Remarks. — If a simple relation exists between the values of 
one variable and the corresponding values of another variable 
dependent upon the former, their relation can always be shown 
graphically by a curve constructed as above. If the curve does 
not pass through all the points, the variation of the points from 
the average position of the curve is due to experimental errors, 
or to some cause for which a correction may be introduced. If 
the dependent variable changes by equal amounts when the 
independent variable changes by equal amounts (i.e. when the 
relation is a direct proportion), the " curve " becomes a straight 
line. 

The particular kind of curve obtained in this exercise is 
known as a parabola, and its mathematical law is expressed by 
the general equation, y 2 = ax, where y is any ordinate, x its 
corresponding abscissa, and a some constant. 

To determine whether the curve, which seems to be a parab- 
ola, is really a parabola, plot a new curve in the same manner 
as above, using the square root of the lengths for the x's (ab- 
scissas) and the corresponding values of t for the y's (ordinates). 
If the resulting curve is a straight line, then it can be shown by 
the geometry of similar triangles that the x's are directly pro- 
portional to the y% as mentioned above. This proves that the 
law of the pendulum is 

1 *■ '>. = etc 



y/l v7j y/l 



52 LABORATORY EXERCISES IN PHYSICS 

Squaring, we have 

/2 f 2 f 2 

— = - 1 - = -2- , etc. = a, some constant. 

Therefore if any value of t be represented by y, and its 

corresponding value oil bj x, - = a, .\ # 2 = ax, the law of the 

parabola, as above. Thus, by the graphic method of exam- 
ining our numerical data, we have shown that the law of the 
pendulum is expressed by the law of the parabola. That is, 
putting it in ordinary language, instead of the language of 
algebra, the squares of the periods of pendulums at a given 
place are directly proportional to the corresponding lengths. 
The constant in the last column of your experimental results is 
the square root of the constant, a, of the equation y 2 = ax. 

This exercise shows how the law of the pendulum might have 
been discovered by the graphic method, had it not been already 
known to you; and it also illustrates how convenient is the 
graphic method when employed by skilled mathematicians in 
examining relations between physical quantities. 



Part D 

INFLUENCE OF MASS ON PERIOD 

Purpose. — The purpose is to find whether a change 
in the mass of the bob makes any change in the period 
of oscillation, the length and location being constant. 

Apparatus. — This consists of a hollow brass cylin- 
der * which has a bail by which it may be suspended, 

* Instead of the bob above described, there may be supplied a 
small cylindrical tin box, having a screw-top. The wire is passed 
through a small hole punched in the centre of the top, and is sol- 
dered on the under side. The jar is to be filled with sand for the 
first trial, and with shot for the second. It must be full both times. 



MECHANICS OF SOLIDS 53 

and into which a solid brass cylinder just fits. The 
cylinder is suspended by a fine steel wire, a meter or 
more in length, which is gripped at its upper end in 
a suitable clamp or a small vise. The timepiece of 
Part A is used. 

Operations. — (a) Remove the solid cylinder and 
observe, as in Part A, the number of oscillations in 
100 seconds, or take the time of 100 oscillations, as 
preferred. 

(6) Replace the solid cylinder, and repeat the 
operations. 

Data. — Tabulate the values of total time, number 
of oscillations, and the period deduced therefrom as 
observed from a series of trials. 

Inference. — (a) Does the period remain practically 
constant ? 

(6) Is this what you might have expected from 

consideration of the fact that the formula t = ir^- 
contains no expression for mass ? ^ 

(c) State the law which has been verified. 

Sources of Error. — In addition to the errors of 
Part A, the most likely one arises from the stretching 
of the wire by the additional weight of the solid cyl- 
inder. To avoid this, place a little marker so that 
the bottom of the bob just touches it when the empty 
cylinder is at rest in its lowest position. After the 
solid cylinder has been replaced, observe again the 
position of the bottom of the bob with reference to 
the marker, and if the wire has stretched, shorten it 
at the clamp till it is of the same length as before. 



CHAPTER III 

MECHANICS OF FLUIDS 

Exercise Number 12 
relative density by the submersion method 

References 

A 153, 155, 156, 160 GE 114-116 H & W 59, 112, 113 

C 124 GP 146-149 L 169-176 

C & C 134-136, 140-144 H 143, 146-150 S 26-31 
W & H 72, 73, 75 

Purpose. — The purpose of this exercise is to de- 
termine (a) the relative density of a solid and (5) the 
relative density of a liquid with reference to water as 
a standard. The solid chosen is to be denser than 
water or the liquid, and is to be insoluble in either. 
Under these conditions the methods are of general 
application. 

Part A 

OF A SOLID 

Apparatus. — The apparatus provided consists of 
balance and weights, thread, a jar or beaker of dis- 
tilled water, and the cylinder used in Exercises 2 and 
3. Diagram the apparatus as used. 

Operations. — (a) Make a slip-noose at one end of 
the thread and a loop at the other end. 

54 



MECHANICS OF FLUIDS 



55 



(6) Pass the loop over the hook * on the bottom of 
one of the scale pans, adjusting it to such a length 
that the solid, when suspended in 
the noose, will hang 10 or 15 cm. 
below the pan. 

(<?) Adjust the scales to equilib- 
rium with the thread so attached. 

(<#) Suspend the solid, or place it 
in the pan, and obtain its weight, W. 

(V) Suspend the solid in the jar of 
water, adjusting the scales so that it 
is totally submerged when the beam 
is horizontal, but touches neither the 
sides nor bottom of the jar ; and 
obtain the apparent weight, W v 

(/) If time permits, suspend the 
solid from the other pan, and obtain 
the values of W and W 1 as before, 
using their mean values, as in Exer- 
cise 3. Ordinarily the arithmetical mean will do, 
because it does not usually differ from the geometric 
mean by an amount greater than that of the unavoid- 
able errors of experiment. 




Fig. 13. 



* If the balance pans have no hooks, the thread may be suspended, 
as shown in Fig. 13. If suspended in this way from the trip scales, 
the scales must be mounted on a box or other support, with the end 
of the balance projecting over the end of the box. The loop must 
be long enough so that the thread will not touch the base of the 
balance or any part of its support. A bit of soft wax will keep the 
thread in place. If the balances have the perforated horn pans, 
close the holes with corks and put small screw-hooks into the corks 
from below. 



56 LABORATORY EXERCISES IN PHYSICS 
Data. — Record data in the tabular form below. 

Numerical Data 



Substance of the solid 




Form of the solid 




Number of the solid 




Weight, W 




Apparent weight in water, W x 




Buoyant force, W — W 1 








~" J ' W -W 1 


Density from Exercises 2 and 3 





Part B 

OF A LIQUID 

Apparatus. — A jar of the liquid* whose relative 
density is to be determined is added to the apparatus 
of Part A. 

Operations. — The only additional operation is that 
of obtaining the apparent weight of the solid while 
submerged in the liquid under examination. 

Data. — Tabulate these as below, usiug the values 
of TTand W x obtained in Part A. 

* E.g. a saturated solution of common salt or of copper sulphate. 
Iron and lead cannot be used in the latter liquid, as it acts upon 
them chemically. 



MECHANICS OF FLUIDS 



57 



Numerical Data 



Substance of the solid 




Form of the solid 




Number of the solid 




Weight, W 




Apparent weight in water, JPj 




Buoyant force of water on solid, W — W x 




Apparent weight in liquid, W 2 




Buoyant force of liquid on solid, W — W 2 




Relative density of liquid, — — -? 




Xame of liquid 



Sources of Error. — These are as follows : (a) Im- 
perfections of the balances and weights. 

(6) Parallax in observing the pointer of the scales. 

(e) Friction of the liquid on solid and thread, 
reducing the sensitiveness of the balance. 

(cZ) Buoyant forces of the liquids on the thread. 
In very accurate work a silver or platinum wire is 
used, and corrections are made for the buoyant forces 
on it. 



58 LABOBATOBY EXERCISES IN PHYSICS 

(e) Buoyant force of air on the solid. When 
great accuracy is sought, the corrections for deducing 
the weights in a vacuum are applied. 

(/) Water may not be pure and at 4° C. Correc- 
tions for temperature can be applied. 

Inferences. — (a) If, by definition, 

, n ,. A weight of the body 

specific gravity = — . 1 . ? = = J — l — - , 

r ° J weight oi an equal volume ot water 

can the numerical value of this ratio be obtained by 
taking the numerical value of the expression 

weight of the body 9 w 



buoyant force of water on the body ' 

(5) If, by definition, specific gravity of a liquid 

_ weight of a given volume of the liquid 
weight of the same volume of water 

can the numerical value of this ratio be obtained by 
taking the numerical value of the expression 

buoyant force of the liquid on a solid ? w , ? 
buoyant force of water on the same solid ' ^ ' 

(<?) Is the numerical value of the relative density 
the same as that of the specific gravity ? Why ? 

The density of a substance is one of its most im- 
portant characteristics. The knowledge of it is often 
indispensable, not only to the scientist, but also to 
the manufacturer, merchant, and consumer. Find 
some instances. 



MECHANICS OF FLUIDS 



59 



Exercise Number 13 



RELATIVE DENSITY BY THE FLOTATION METHOD 





Keferexces 




A 154, 157, 160 


GP 15<) 


L 172. 171, 177 


C & C 138-144 


H 144, 150 


S31 


GE117 


H k W 113 


W & H 71, 75 




Purpose. — In this exercise it is proposed (cC) to 

determine the relative density of a wooden rod by 
applying the principle of flotation, 
and (5) to determine the relative 
density of a liquid by using the 
rod as a constant weight by hydrom- 
eter. 

Apparatus. — Qci) The rod of 
wood whose relative density is to 
be found must be of uniform cross- 
section, and should be given a thin 
coating of paraffin, so that it cannot 
absorb the water or other liquid. 

(J) A supply of distilled water 
and of the liquid, each in a tall 
glass jar. 

(<?) A support for floating the 
rod upright consists of a piece of 
a meter rule, with two screw-eyes ^-v 
set horizontally into the front of Lj J 

it. A spring: clamp attached to the *^= ^^ 



spring clamp 

back of it holds it firmly against Fig. u. — Showing 

, , . , , , . the rod and support 

the side ot the jar. in position. 



•4 



60 LABORATORY EXERCISES IN PHYSICS 

Part A 
OF A SOLID 

Operations. — (a) Place the support vertically in 
the jar of water, and see that the clamp holds it 
firmly in position. 

(5) Pass the rod vertically downward through 
both screw-eyes, and carefully allow it to sink just 
as far as it will. Tap very gently on the side of the 
jar, or support, in order to overcome any friction that 
may interfere with free motion of the rod upward or 
downward. 

(<?) Take two readings, on the support, of the 
position of the lower end of the rod, and the same 
number of readings of the upper level of the water. 
Wipe the rod dry, reverse it and repeat, taking four 
readings as before. Take the mean of the four 
readings for the lower end, and also the mean of the 
four readings for the water level. Avoid parallax 
by keeping the eye on a level with the point at 
which the reading is taken. If the surface of the 
water is elevated by capillary action near the rod, 
give the rod a fresh coat of paraffin. 

(cT) With a metric rule take four measurements 
of the total length of the rod. 

Data. — Enter the data in a tabular form like that 
below. The length of the part submerged is obtained 
by taking the difference between the mean upper 
and mean lower readings. The relative density of 
the wood is calculated by dividing the length of the 
part submerged by the length of the entire rod. 



MECHANICS OF FLUIDS 



61 



Numerical Data 





Eeading 

Lowek End 


Beading 

Water Surface 


Length of 

Submerged 

Part 


Length of 
Entire Eod 


1 










2 










3 

j 








4 








Mean 










Name of substance 




Relative density 





Theory. — Let TT= weight of rod, m its mass, I its 
length, and V its volume : let W = weight of Avater 
displaced by submerged part, m' its mass, v f its vol- 
ume, V its length (i.e. the length of the submerged 
part of the rod); and let D be the density of the 
substance of the rod, D 1 the density of water, and a 
the cross-sectional area of the rod. 

Then W= W (Principle of Flotation) ; and since 
W = m, and W = m' (mass is numerically equal to 
weight), 

m = m'. (Why 9 ) 



62 LABORATOBY EXERCISES IN PHYSICS 

Also m = VD and m' = V r D' ; 

.\ VD=VD'. (Why?) 

But V=al and V = aV . (Geometry.) 

Whence, by substitution, 

alD = aVD 1 ; 

and dividing by alD\ 

D V 
Relative Density = — =y. 

Evidently this method applies to any substance 
less dense than water, provided it be cut of uniform 
cross-section, with its bases approximately perpen- 
dicular to its length. 

Part B 
OF A LIQUID 

Operations. — Qd) Wipe the rod and support 
(Why ?), and repeat operations (a), (5), and Qc) 
of Part A, but with the rod floated in the liquid 
whose relative density is to be determined instead 
of in water. 

In a tabular form like that on the following page 
enter the data thus obtained, together with the nec- 
essary datum from Part A. 

(J) Calculate the relative density by dividing the 
mean length of the part submerged in water by the 
mean length of the part submerged in the liquid, in 
accordance with the theoretical deduction above. 



MECHANICS OF FLUIDS 



63 



Numerical Data 



Trial 


Reading 
Lower End 


Reading 
Liquid Level 


Length of 
Part Submerged 


1 








2 








3 








4 








Mean 








Length of part submerged in water 




Eelative density of liquid 




Name of liquid 





Theory. — Let IF, iff", J 7 ", a, and I represent, respec- 
tively, the weight, mass, volume, sectional area, and 
length of the displaced liquid; and let IF 7 , M 1 , V\ 
a, and V represent, respectively, the same quantities 
for the displaced water. Also let D and D f be the 
densities of the liquid and of water. 

Then W=W f (since by the Principle of Flotation 
each is equal to the weight of the rod) ; and by rea- 
soning precisely similar to that of Part A, 

D V 

— = — = Relative Density df the Liquid. 



64 LABORATORY EXERCISES IN PHYSICS 

Sources of Error. — Errors result from (a) parallax, 
and errors of judgment in reading (personal equa- 
tion). (6) The rod and support may not be exactly 
vertical. (<?) Slight friction may prevent the rod 
from floating freely. (<#) The rod may not be 
exactly vertical. 

Lessons. — This exercise gives valuable practice in 
manipulation, and in the application of the principle 
of flotation for the rapid determination of density 
where refined methods are not available. It also 
illustrates the principle which underlies all constant 
weight hydrometers. 

The principle of flotation is fundamental in ship 
designing. The weight of a vessel equals its " dis- 
placement." A battleship designed to carry heavy 
armour and heavy guns must have a large displace- 
ment and great stability. This necessitates increased 
draught and breadth of beam. The naval designer 
must compromise between weight and speed. Com- 
pare a protected cruiser with a first-class battleship. 

Additional Work. — Other woods and other liquids may be 
given, if desired. 

Note. — If the support is not at hand, the rod may be sup- 
ported laterally by the ringer tips. A ring of fine silk thread 
may be adjusted on the rod to mark the upper level of the 
liquid, and the length of the part that was submerged measured 
by a rule. Paraffining the rod and support serves the additional 
purpose of preventing the liquid from adhering to them, and 
thus disturbing the true level of the liquid. It is desirable to 
use the same liquid that was chosen for Exercise 12, so that the 
results by the two methods may be compared, and a check on 
their accuracy thus secured. 



MECHANICS OF FLUIDS 



65 



Exercise Number 14 



RELATIVE DENSITY OF A LIQUID BY HARE'S METHOD 
References 



A 165, 166 


GP 131, 144, 149 


S 48, 62 


C 131-133 


H pg. 139, 159-161 


W&H 77 


C & C 146-148 


H & W 121, 153 




GE 102-104 


L182 





Purpose. — The purpose of this exercise is to deter- 
mine the relative density of a liquid by the method 
of balancing columns supported by atmospheric 
pressure. 

Apparatus. — The apparatus consists of two glass 
tubes, each nearly a meter long, and joined by rubber 
tubing to the two branches of 
a three-way tube (made from a 
T-tube bent as shown) ; and to it 
is attached a long rubber tube 
terminating in a glass mouthpiece. 
The glass tubes are secured to a 
meter stick by rubber bands, and 
the meter stick is fastened in a 
vertical position by screw clamps 
(or by any convenient support). 
Its end rests on the table-top. 
The ends of the glass tubes should 
terminate in short rubber tubes 
which dip into two beakers or small 
jars, one containing distilled water, and the other the 
liquid whose relative density is to be determined.* 

* Use the same liquid as in Exercises 12 and 13. 



) f 

3 




foil 





Fig. 15. — Appara- 
tus for the determina- 
tion of relative density 
by Hare's method. 



66 LABOBATORT EXEBCISES IN PHYSICS 

A pinch-cock, or a Hoffman screw-compressor, is 
placed above the mouthpiece on the rubber tube, to 
prevent the ingress of air after it has been withdrawn. 

Operations. — (a) Remove, rinse, and replace the 
mouthpiece. 

(6) Open the pinch-cock, remove air from the 
tubes until the columns of liquid stand a little below 
their upper ends. 

(Why do the liquids rise to unequal heights? Which liquid 
is the denser ?) The air is to be removed by suction at the 
mouthpiece a little at a time, so as never to allow the liquids 
to be pushed over the bend. (Why?) In case such an acci- 
dent should occur, remove the entire apparatus to the sink and 
rinse it thoroughly. The columns can be held at any desired 
point, while the pinch-cock is being adjusted, by closing the 
end of the mouthpiece with the tongue. 

(c) After closing the pinch-cock, watch the appara- 
tus for a moment, to see that it does not leak, then 
read on the rule the positions of the upper ends of 
the columns. Read to tenths of millimeters, being 
careful to avoid parallax. In like manner read the 
position of the liquid surface in each of the beakers. 
Make each upper and each lower reading from the 
bottom of the meniscus. In reading, it is convenient 
to hold a straight-edged card against the scale and 
tube, with its upper edge parallel to the divisions of 
the rule. The two lower readings should be taken 
as nearly as possible at the same instant, and so also 
should the two upper readings. 

(c?) Let the liquid columns run down a few cen- 
timeters, and repeat the observations. Take as many 
sets of readings as time permits. Remember that 



MECHANICS OF FLUIDS 



67 



the longer the columns, the less is the percentage 
error. In order to eliminate the small error due to 
capillary action, it is well to have a short piece of 
tubing, like that of the apparatus, placed in each 
beaker, and to take each lower reading at the bottom 
of the meniscus in the short tube. This tube should 
be held vertically, and not too near the long tube or 
to the side of the beaker. 

(e) Remove the pinch-cock after completing the 
readings. 

Data and Calculations. — Record the name of the 
liquid, the readings, and the derived data in a tabu- 
lar form like that below. The height of each col- 
umn is obtained by subtracting the smaller reading 
from the greater. The relative density for each set 
of readings is obtained by dividing the height of the 
water column by the height of the liquid column. 
Compute the mean relative density from the num- 
bers in the last column, and record it below the data, 
together with the values of the relative density of 
the same liquid obtained in Exercises 12 and 13. 

Numerical Data 



Water 


Liquid 


Lower 
Reading 


Upper 
Reading- 


Height of 
Column 


Lower 
Reading 


Upper 
Reading 


Height of 
Column 


Relative 
Density 

















68 LABORATORY EXERCISES IN PHYSICS 

Theory. — Let m, v, a, A, and D represent respec- 
tively the mass, volume, sectional area, and height 
of the liquid column ; and let m 1 , v\ a, h f , and 
D f represent the same quantities for the water 
column. 

Then since they are balanced by the same result- 
ant atmospheric pressure, the weights and there- 
fore the masses of the two columns are equal, i.e. 

But m = vD = ahD 

and w! = v f D f = ah r D r . (Why ?) 

.-. ahD = ah ! D f ; (Why?) 

and hD = h f D f . (Why?) 

D h f 
Whence — = - = Relative Density. (Why ?) 

Sources of Error. — (#) Errors may arise from 
temperature changes. In very accurate work cor- 
rections must be applied for expansion ; or the col- 
umns must be cooled to 4° C. 

(J) Dirt in the tubes may affect the amount of 
capillary elevation or depression. 

(<?) There will also be errors due to parallax and 
personal equation. 

Lesson. — Besides useful laboratory practice this 
exercise affords valuable practice in applying the 
principles of fluid equilibrium. 



MECHANICS OF FLUIDS 



69 



Barometer 



i 



«D 



Reading the Barometer. — (a) Turn the screw to 
the left until the mercury in the cistern is seen to 
withdraw below the little ivory point at B. This 
ivory point represents the zero end of 
the scale that is attached to the metal 
case. 

(5) Looking so that the line of sight 
is tangent to the mercury in the cis- 
tern, slowly turn the screw to the 
right until the ivory point just meets 
its image reflected in the mercury. 

(V) By turning the screw D from 
you, raise the lower edge of the sliding 
(or vernier) scale, (7, until you can 
see over the upper surface of the 
mercury column. 

(<#) Place the eye on a level with 
the highest point of the mercury col- 
umn, and by reversing the screw D 
lower the vernier till its zero line 
appears just tangent to the curved 
surface of the mercury. 

(e) Read the scale and vernier precisely as directed 
for the vernier slide caliper, Exercise 2, Part B. 

(/) If the barometer reading is to be taken in 
inches instead of in centimeters, note that inches and 
tenths are measured by the fixed scale and hundredths 
of inches by the vernier. 



o 

Fig. 16. — U.S. 
Weather Bureau 
Standard Station 
Barometer. 



70 LABORATORY EXERCISES IN PHYSICS 

Correction for Temperature. — The temperature of the room 
being higher than 0° C, the mercury column and the scale by 
which it is measured are both expanded by the heat, and there- 
fore are longer than they would be at 0°. As the readings of 
air pressure are customarily based upon the supposition that the 
temperature of the mercury is zero, it is usual to observe the 
temperature of the barometer by means of the " attached ther- 
mometer " (E, Fig. 16), and to correct the observed height of 
the column for the error due to expansion. The correction is 
the difference between the expansion of the mercury column 
and that of the brass scale by which it is measured. (Would 
a correction be necessary if both expanded equally?) Since the 
temperature of the room is above zero, and since the mercury 
expands more than does the brass, the observed height is too 
great, and the correction is to be subtracted. The amount of 
the correction is jointly proportional to the length and to the 
temperature of the mercury column. 

The corrections for all pressures and temperatures have been 
calculated, and are published in the tables of the United States 
Weather Bureau. Unfortunately, the pressures are expressed 
in inches and the temperatures in Fahrenheit degrees. So that 
the barometer should be read accordingly, if its indication is to 
be thus corrected. 

To find the correction for temperature, consult the Table for 
Reduction to 32° F., in accordance with the rule given below. 

In the vertical column at the left find the temperature that 
was observed on the attached thermometer. Follow the line of 
this number to the right till you reach a column of figures, 
headed by the pressure-reading that you observed. In this 
vertical column, the number directly opposite your attached 
thermometer-reading is the correction required. If the exact 
temperature and pressure that you observed are not shown in 
the table, select the nearest values that are tabulated. 

Other Corrections. — When readings simultaneous at different 
places are to be compared, they are all reduced to what they 
would be at sea level. The capillary depression of the mercury 
in the tube is corrected by permanently lowering the scale. 



MECHANICS OF FLUIDS 



71 



A 168, 169 
C 136-142 
C & C 161-163 
GE 107 



Exercise Number 15 

BOYLE'S LAW 

Part A. — Verification 

References 

GP 131, 137 
H 166-168 
H & W 124, 125 
L 189-190 



S 63-65 

W & H 79-81 



Purpose. — The purpose of this exercise is to deter- 
mine the relation between the volume 
of a given mass of gas, at constant 
temperature, and the pressure under 
which it is confined ; or, more briefly, 
it is to verify the law of Boyle. 

Apparatus. — (a) A glass tube about 
30 cm. long, closed at one end by a 
capping disk and clamp screw, is joined 
by about a meter of rubber gas tubing 
to another glass tube of the same bore, 
open at both ends and about 50 cm. 
long. This composite tube is mounted 
on a board so that the two sections of 
glass tubing are vertical, and can slide 
up and down on opposite sides of a 
meter rule. They are suspended by 
a cord, sliding over screw hooks at the 
top of the board, and can be held in 
position by stiff rubber bands. The fig. 17. — Ap- 
apparatus contains as much mercury paratus for ver- 

•n n-n • • • r ^Y^ n S Boyle's 

as will nil it to the middle points ot Law. 



72 LABORATORY EXERCISES W PHYSICS 

the two glass sections when these points are at the 
same level. 

This adjustment should be made by the teacher (or, if by a 
student, under the eye of the teacher) as follows : (1) Set the 
tubes so that the middle points of the glass sections are at the 
same level. (2) Turn the clamp screw backward, and loosen 
the capping disk so as to allow free passage of air under it. 
(3) Pour mercury through a funnel into the open section till it 
stands at the middle points of the two glass sections. (4) Ad- 
just the capping disk, and force it down by the clamp screw till 
it closes the tube air-tight. The board is secured to the table 
in an upright position by screws, or by clamping in a vice or 
carpenter's hand-screw. A mercurial. 

(5) A mercurial, or aneroid barometer, and a 
thermometer are provided. 

Operations. — (a) Note the temperature of the air 
near the apparatus. It should be kept constant 
throughout the experiment. 

(5) Adjust the open tube at the greatest conven- 
ient height, and the closed tube at the least. Read 
and record the following : (1) The height of the 
barometer, B, in cm. ; (2) the level, s, of the 
mercury in the open tube ; (3) the level, s ? , of 
the mercury in the closed tube ; (4) the level, e, of 
the upper end of the air column inside the closed 
tube. Read from the middle of the meniscus, esti- 
mating, if practicable, to the hundredth of a centi- 
meter. 

(<?) Lower the open tube and raise the closed tube 
each a few centimeters, and take a new set of four 
readings as before. 



MECHANICS OF FLUIDS 73 

(<f) Continue the process until the open tube is at 
the lowest convenient point, and the closed tube at 
the highest. Obtain one set with the mercury at the 
same level in both tubes. 

Data and Calculations. — Let a represent the inter- 
nal sectional area of the glass tubing, I ( = e — $'), the 
length of the column of confined air, and h (= s — s', 
positive or negative), the difference of level between 
the two mercury surfaces. 

(a) Record in tabular form, making a column for 
the different values of each of the following quan- 
tities : s, &\ e, Z, A, i?, B + A, (i? + K) x I. 

(5) State whether the values of (1? + K) x I are 
equal within the limits of experimental errors for all 
values of B + h and the corresponding values of I ; 
i.e. is the product (i? + K) x I a constant ? 

Theory. — Note that V, any volume of the mass of 
confined air = al, and that P, the corresponding re- 
sultant downward pressure (in grams) of the atmos- 
phere and mercury upon the confined air = the volume 
of the mercury column (5 + K)x specific gravity of 
mercury = a (jB + K) 13.6 (Why ?) Evidently, now 
if (B + K) I = K 1 , a constant, then alxa(B + h) 13.6 
= K, another constant. (Because it consists of K 1 
and the constant factors a and 13.6.) Substituting 

V and P for their values al and a QB + K) 13.6, we 
have VP = K. For similar reasons, V'P r , any prod- 
uct of another volume of this mass of gas and its 
corresponding pressure = K. .\ VP = V'P'. Also, 

V P f 
yi=~- (Why?) 



74 LABORATORY EXERCISES IN PHYSICS 

Inference. — (a) Write a general verbal statement 
of the meaning of the equation, VP = K, and also of 

V P' 

the meaning of the equation, — = — 

(5) Do your results verify these two statements ? 

Sources of Error. — These are : (a) Any cause tend- 
ing to change the temperature of the confined air or 
mercury. Hence, avoid letting the hands, the breath, 
or sunshine come into contact with them. 

(J) Parallax. 

(V) Air or other impurities mixed with the mer- 
cury. 

(cT) Leakage, inward or outward, changing the 
mass of confined air. This will not occur if the 
capping disk is tight and the rubber tube is securely 
wired and cemented to the glass tubes. 



Part B 

GRAPHIC REPRESENTATION 
Reference. — Review Exercise 11, Part C. 

Purpose. — It is proposed to plot a curve showing 
the relation between the pressures on a given mass 
of gas and the corresponding volumes, taken from 
the tabulated results of Part A. 

Operations. — (a) Let the ordinates represent the 
values of B + h observed in Part A, and the abscissas 
the corresponding values of I. Choose such a scale 
for the ordinates that the greatest value of B + h 
shall be represented by a line somewhat shorter than 



MECHANICS OF FLUIDS 75 

the length of the page. Also choose such a scale for 
the abscissas that the greatest value of I shall be rep- 
resented by a line somewhat shorter than the width 
of the page. 

(5) Locate the points of the curve and record all 
the data precisely as directed in Exercise 11, Part C. 

Lessons. — If made from accurate data and correctly plotted, 
the curve will be a hyperbola. This is the name given by 
mathematicians to the class of curves which may be represented 
by the general equation xy = A, a constant. 

By inspecting the direction that the curve takes with respect 
to the a; -axis, try to interpret it so as to predict the value of the 
volume which corresponds to zero pressure. Also, from the 
direction which the curve tends to take with respect to the y- 
axis, try to infer the amount of the pressure necessary to reduce 
the volume to zero. Can the curve pass through the origin? 

Notice that you found by your experiment that (B + h)l = K, 
a constant, which equation is identical in form with the above. 
Therefore, if you had not been directed to multiply B + h by I, 
and had no suspicion that the products thus obtained would 
have a constant value ; nevertheless, by plotting the curve and 
getting one whose law is xy = A, you could have learned from 
the curve that xy, the product of any abscissa and its correspond- 
ing ordinate, is a constant quantity. Now, in this particular 
case, (B + h)l is the xy and is therefore a constant. Whence 
by this convenient method of examining your results you might 
have discovered Boyle's Law. 

To find whether or not the curve is really a hyperbola, put 

the equation xy = A into the form y =A f - ) . Since this equa- 
tion is now of the same form as that of the straight line (y = ax), 
it appears that if we plot a new " curve " with the values of y 

for ordinates, and the values of - for abscissas, the line thus 

x 

plotted should be straight. If it proves to be so, we shall know 



76 LABORATORY EXERCISES IN PHYSICS 

that we were correct in thinking that the first curve is denned 
by the equation y = Al-\ or xy = A, and that it is therefore 

a hyperbola as we supposed. Take the values of B + h from 
your tabulated results for the ordinates, and having obtained 

by division the values of -, take them for the abscissas and 

plot a new curve. If the line thus plotted is straight, then 
(since in the case of a straight line the abscissas are directly 
proportional to their ordinates) it follows that 

1 

(B + h) l = l l = l 2 

(b + h) 2 i i; 

Whence (B + A)^ = (B + h) 2 l 2 . 

That is, (B + h)l is a constant quantity. 
Thus the law might have been demonstrated without previous 
knowledge of it. 



CHAPTER IV 



HEAT 



Exercise Number 16 



THERMOMETER 



References 



A 216-221, 235, 240 

C 131-133, 220-223, 229-232, 

243-245 
C & C 305-315, 331, 337 
GE 126-128, 145, 149, 150 
GP 206-214, 239, 248, 262 



H 235-245, 272, 274,277,286 
H & W 121, 167, 168, 177, 

184, 186, 187 
J 1-9, 12, 41-43, 47, 50-54, 56 
S 83-96, 119, 120, 130, 131 
W & H 90, 94, 99, 102, 104 



ESCAPE 
TUBE 



Purpose. — The purpose of this exercise is to test 
the boiling and freezing 
points of a centigrade ther- 
mometer. 

Apparatus. — This consists 
of a boiler with a tight-fitting 
top terminating in a vertical 
tube, a Bunsen burner, and 
the thermometer to be tested. 
A supply of pure water and 
a vessel of cracked ice or 
snow are also provided. 

Operations. — (a) See to it 
that the boiler is half full of 
water; then fit the cover 

77 




SCREW-CAP 
Fig. 18. — The boiler. 



78 LABORATORY EXERCISES IN PHYSICS 

tightly to it, and also cork the lower or overflow 
tube. 

(5) Holding a lighted match 5 or 6 inches above 
the burner, turn on the gas and allow it to ignite. 
The gas must never be allowed to burn on the inside of 
the tube. Place the flame under the boiler. Be very 
careful not to let the water boil away during the opera- 
tions, or the apparatus will be ruined. 

(<?) While the water is heating place the ther- 
mometer bulb, and all that part of the tube below 
the zero mark, in the mass of cracked ice. Use a 
pencil or a sharp-pointed stick to make an opening 
for the thermometer ; and insert the instrument 
carefully lest it be broken. 

The interstices between the lumps of ice should 
be filled with water. 

Wait till the mercury becomes stationary, and 
then, with great care, read the instrument to the 
tenth of a degree. In order to average the errors 
of observation, take several readings ; and if they 
do not exactly agree, record the mean. Be very 
careful to avoid parallax.* 

The vessel of ice should not be near a flame or a 
radiator. The ice must be kept thoroughly in con- 
tact with the thermometer bulb, and the instrument 
should not be lifted any farther out of the mixture 
than is necessary to observe the top of the mercury 
column. 

* Place the eye so that the division line looks straight at the 
point of reading. If the eye is too high, the lines will be convex 
downward, if too low, convex upward. 



HEAT 79 

(d) Remove the thermometer to the boiler ; sus- 
pend it securely by a wire passed through a cork, 
slowly lower it through the tube at the top of the 
boiler, and close the opening with the cork. The 
bulb should not be in the ivater. Keep your fingers out 
of the steam. Be very careful not to break the glass 
loop by which the thermometer hangs. 

(e) When the thermometer has come to the tem- 
perature of the steam, the mercury will remain sta- 
tionary. After time has been given for this, lift the 
thermometer by the wire till the top of the mercury 
column is just visible, and read its position accurately 
to the tenth of a degree. Take several independent 
readings ; and if the values vary, record the average. 
Now turn off the gas. 

(/) Having first read and recorded the indication 
of the attached thermometer, read and record the 
height of the barometric column in inches ; correct 
it for temperature by the tables of the U. S. Weather 
Bureau ; and reduce it to millimeters by multiply- 
ing by 25.4, the number of millimeters in an inch. 
(Page 70.) 

(#) If time permits, make another determination 
of the freezing point, but be very careful not to trans- 
fer the thermometer to the ice until it has cooled 
considerably . (Why ?) 

(K) Correct the reading of the boiling point for 
atmospheric pressure by adding -^° (which reduced to 
a decimal = .037) for every millimeter by which the 
barometric reading is less than 760, or subtracting this 
amount for every millimeter by which it exceeds 760. 



80 



LABORATORY EXERCISES IN PHYSICS 



Data. — Record in tabular form. 



Numerical Data 


First 
Trial 


Second 
Trial 


Number of the thermometer 






Barometer reading in inches 






* Reading of the "attached thermom- 
eter " in degrees F. 






* Amount of temperature correction in 
inches 






* Barometer reading, corrected for tem- 
perature, in inches 






* Barometer reading, corrected, ex- 
pressed in millimeters 






Boiling point observed during the test 
in degrees C. 






Amount of correction for atmospheric 
pressure in degrees C. 






Boiling point of the thermometer 
tested, at 760 mm. pressure 






Amount of boiling-point error in de- 
grees C. 






Freezing point of the thermometer 
tested in degrees C. 






Amount of freezing-point error in de- 
grees C. 







* In case the teacher directs that the correction of the barometer 
for temperature is to be omitted, the data marked by asterisks will 
not be needed, and the barometer, if provided with a metric scale, 
should be read in millimeters. 



HEAT 81 

Note. — The boiling-point error is found by taking the dif- 
ference between 100° (the correct boiling point at 760 mm. 
pressure) and the boiling point of the thermometer that is 
being tested (also at 760 mm. pressure). In order to correct 
the readings, the amount of this error is to be added if the 
thermometer reads too low or subtracted if it reads too high. 

The amount of the correction for n° is of the correction 

100 

for 100°. Thus, if the correction at the boiling point is .5°, at 
70° the correction is ffo of .5° ■= .35°. 

The freezing-point error is the difference between the freezing- 
point reading and 0° (the correct freezing point), to be added if 
the thermometer reads too low and to be subtracted if it reads 
too high. 

If both the freezing and the boiling points are in error, and 
a reading is to be corrected, the freezing-point correction must 
first be applied, and then the boiling-point correction, as directed 
above. 

Sources of Error. — The principal sources of error 
are parallax and personal equation. Errors may also 
arise from taking the readings before the thermometer 
acquires the temperature of the ice or of the steam. 

Lessons. — This exercise is intended to give famil- 
iarity with the construction and elementary theory of 
the thermometer and with some of the precautions 
and corrections which are to be regarded in its use. 

The exact measurement of quantities of heat en- 
ergy involved in chemical and engineering processes 
is of fundamental importance in our modern material 
development, as well as in science. Much of it has 
been gained through observations by mercurial ther- 
mometers. When calibrated by comparison with a 
standard air thermometer, a mercurial thermometer 
can be made to give very accurate readings. 



82 LABORATORY EXERCISES IN PHYSICS 

Exercise Number 17 
specific heat 

References 

A 225-226, 309-311, 242, 247 H 281-283, 253, 254, 258, 262 

C 246-248, 224-226, 229-232 H & W 205-210, 197-199, 202 

C & C 325-328, 343-347, 350, 351 J 35-40, 68-70, 86-91 

GE 130-135, 158, 159, 163 S 113-118, 154, 157 

GP 219-224, 257, 382 W & H 107-109, 121-123, 125 

Purpose. — In this experiment the specific heat of a 
metal is to be determined by the method of mixtures. 

Apparatus. — This consists of the following : — 

(a) Balance, weights, and pincers. 

(6) The boiler of Exercise 16, with the cup which 
fits into the boiler in place of the cover. 

(<?) A Bunsen burner. 

(c?) A calorimeter, consisting of a cup of thin brass, 
nickel plated, supported upon a cork in a jar or box, 
and packed around with cotton-batting or felt. 

(e) Perforated wooden covers for the cup and 
calorimeter. 

(/) Two thermometers. 

Materials. — The substance whose specific heat is 
to be determined, may be in the form of punchings 
or short clippings of wire or a loose roll of the sheet 
metal. A supply of cold water should also be at 
hand. 

Operations. — (a) Half fill the boiler with water 
and place the Bunsen flame under it. 

(5) See that the metal has been thoroughly dried, 
either on top of a radiator, or in a drying oven, and 



HEAT 83 

weigh it to .1 g. If the metal is in loose form, it 
may be weighed in the calorimeter. 

(c) Transfer the metal to the cup, insert the latter 
in the boiler, put on the cover, and cautiously thrust 
the thermometer through the perforation into the 
midst of the metal. 

(cT) Weigh the calorimeter ; place in it the amount 
of water specified by the instructor ; and, having 
dried the outside, weigh it to .1 g. Place a ther- 
mometer in the water, stirring it occasionally. 

(e) When the temperature of the metal has become 
stationary, see that everything is in readiness for 
quickly transferring the metal and water to the 
calorimeter. It is best to have the boiler at the 
right hand, the calorimeter at the left. 

(/) Xow read the temperature of the water and the 
metal to .1°, as nearly as possible at the same moment. 

(g) Immediately after these temperatures are taken 
remove the thermometers, slightly tilt the calorim- 
eter toward the cup with the left hand, carry the 
cup, with the right hand, toward the calorimeter, 
and empty the metal into it, by quickly inverting 
the cup over the calorimeter. Instantly cover the 
calorimeter ; insert its thermometer through the 
perforated cover; and cautiously stir the metal and 
water together by means of the thermometer, watch- 
ing the mercury column attentively. 

(K) When the temperature has reached its highest 
point, if ascending, or its lowest if descending, record 
its reading to .1° as the temperature of the mixture. 

(z) Dry the calorimeter and return the metal. 



84 LABORATORY EXERCISES IN PHYSICS 

Remarks. Calculations. — (a) Great care should be taken 
not to spill any of the metal or water after it has been weighed. 
(Why?) 

(b) In this exercise two students can work together, divid- 
ing operations so as to save time, especially at critical moments. 
Thus the first may read the temperature of the metal and 
transfer it to the calorimeter, the second taking the tempera- 
ture of the water, and so on throughout. The division of labor 
should be planned before beginning the experiment. 

(c) The mass of the water is obtained by subtracting that 
of the calorimeter from that of the calorimeter and water ; and 
that of the metal is obtained in a similar manner. 

(d) The relative amounts of metal and water should be so 
chosen as to have the mixture come as nearly as possible to the 
temperature of the room. Thus the errors due to radiation 
and conduction will be nearly eliminated. (Why?) 

To secure the best results, the water should be ten de- 
grees or more below the temperature of the room; and the 
relative masses, so chosen that the mass of the water multi- 
plied by the difference between its temperature and that of the 
room equals the mass of the metal multiplied by the difference 
between its temperature and that of the room, multiplied by 
its specific heat. The teacher may well make a preliminary 
experiment and calculation, and roughly indicate the amounts 
of metal and water. The actual amounts will necessarily 
depend on the size of the calorimeter and the kind of metal 
used. For a calorimeter of about 350 cc. capacity, 300 g. 
of copper and 100 g. of water are approximately the right 
proportions. 

(e) If the water is not cool enough to give a suitable tem- 
perature range (at least 10°), it should be kept cool by a bit of 
ice. No unmelted ice should remain in the calorimeter, however, at 
the time of mixing. 

(/) If but one thermometer is available, the temperature of 
the metal must be taken when it has become stationary, and 
the thermometer transferred to the water in order to get the 
temperature of the water and calorimeter. 



HEAT 



85 



Data. — Tabulate the quantities as indicated below. 



Name of metal 




Temperature of metal 


i m 


°c 


Temperature of mixture 


t 




Temperature rauge of metal 


tra t 




Mass of metal and calo- 
rimeter 




g 


Mass of calorimeter 


■ M e 


Mass of metal 


Mm 




Amount of heat given out 
by metal 


S m X MmX {tm — t) 


calories 


Temperature of mixture 


t 


°C 


Temperature of water 


tv: 




Temperature rauge of water 


t — tw 




Mass of water and calo- 
rimeter 




o - 


Mass of calorimeter 






Mass of water 


M w 




Amount of heat absorbed by 

water 


1 X Mn, X (t — tw) 


calories 


Temperature of mixture 


t 


°C 


Temperature of calorimeter 


tc(=t w ) 




Temperature range of calo- 
rimeter 


t — tc 




Mass of calorimeter 


Me 


or 
S 


Amount of heat absorbed by 
calorimeter 


|X .09x^fcX(t — tc) 


calories 


Specific heat of the metal 


Sm = 





86 LABORATORY EXERCISES IN PHYSICS 

Heat Equation. — Equate the total amount of heat 
given out by the metal with the total amount ab- 
sorbed by the water and calorimeter. (Why?) 

S m is the only unknown quantity. Solve the 
equation and find it. 

Sources of Error. — (a) Those involved in the 
temperature readings are most important, an error 
of .1° in a range of 10° amounting to lfo. Hence the 
temperature range of the water should be made as 
large as practicable. (How?) 

(5) Errors also occur in mass determination, and 
from losses or gains of heat by radiation and con- 
duction. 

(<?) Since the calorimeter does not wholly come 
into contact with the mixture, only part of it is sub- 
ject to the entire temperature range. If less than 
half filled it is fair to assume that half its mass 
changes temperature ; and the error involved in this 
assumption is small, because its thermal capacity is 
relatively small. If a larger portion is filled, a cor- 
respondingly larger fraction should be assumed. 

(d) Any loss of time in mixing, after reading the 
temperatures, and any loss of metal or water by 
spilling causes errors. (Why ?) 

Lessons. — Practice is given in the determination 
of an important physical constant, and in the use of 
the requisite apparatus, and in handling the equa- 
tions pertaining to the transference of heat units 
when temperature changes take place. 

Try to explain the enormous effects of the large 
specific heat of water on climate. 



HEAT 87 



Exercise Number 18 
latent heat of fusion 





References 




A 244, 245 a 


GE 145-148 


J 43 


C249 


GP 239, 243 


S 119 


C & C 329-333 


H284 

H & W 211, 219, 220 


W & H 112, 114 



Purpose. — The latent heat of fusion of ice is to be 
determined. 

Apparatus. — The boiler, calorimeter, scales, 
weights, pincers, and two thermometers are needed. 

Materials. — The materials used are cracked ice, or 
snow, and water. 

Operations. — (a) Place a thermometer in the calo- 
rimeter, and, after a while, note its temperature. 

(6) Thoroughly cleanse the boiler, if necessary; 
half fill it with water and heat it. 

(e) Weigh the calorimeter. 

(d) When the water is nearly at the boiling point, 
pour into a beaker as much as will fill about two- 
thirds of the calorimeter, and determine the mass of 
the beaker and water. 

(e) Meantime, have ready on a cloth or blotting- 
paper, in the coolest place available, about as much 
cracked ice as, when melted, will fill one-third of the 
calorimeter. It is to be kept as dry as possible till 
used. 

(/) When the water has cooled to about 70° C, 
take its temperature to the tenth of a degree, and 



88 LABORATORY EXERCISES IN PHYSICS 

immediately pour into the calorimeter the ice, and 
then as much of the warm water as will nearly fill it. 
Instantly, put on the perforated cover, insert a ther- 
mometer, and with it keep stirring the mixture until 
the ice is melted. Stir gently, so as not to break the 
thermometer. 

(#) Watch the mercury, which will become sta- 
tionary for a moment just as the ice disappears ; at 
this moment read and record the temperature of the 
mixture. 

Qi) Weigh the calorimeter and its contents ; also 
weigh the beaker with any water that may have 
remained in it. 

Calculations. — To get the mass of the water used, 
subtract the mass of the beaker and water remaining 
in it from the mass of the beaker and water before 
pouring. 

To get the mass of the ice, add the mass of the 
water to that of the calorimeter, and subtract this 
sum from the combined mass of the calorimeter and 
its total contents. 

The temperatures should be read as accurately as 
possible to the tenth of a degree. 

The weighings are more than sufficiently accurate 
if made to the tenth of a gram. (Why ?) 

Data. — Tabulate the observations as indicated 
on the following page. The factor .09 in the quan- 
tity of heat gained or lost by the calorimeter is the 
specific heat of the brass of which the calorimeter 
is made. 



HEAT 



89 



Temperature of water 


tw 


o 


Temperature of mixture 


t 


o 


Temp, range of water 


tw—t 


o 


Mass of beaker and water 




g- 


Mass of emptied beaker 




g- 


Mass of water 


Miv 


g- 


Heat given out by water 


1 x M w x (tw — t) 


calories 


Temp, of calorimeter 


U 





Temperature of mixture 


t 


o 


Temp, range of calorimeter 


(tc-t 

\ or 

* t— tc 


o 


Mass of calorimeter 


Mc 


g- 


„ . j ) by calorim- 
Heat j or > J 

' gained ' 


( .09 X M C X (t c — t) 

I or 

' .09 x M c X (t - t c ) 


calories 


Mass of calorimeter and 
total contents 




g- 


Mass of calorimeter and 
water 


Mc + M w 


g- 


Mass of ice 


Mi 


or g 


Heat absorbed by ice in 
melting 


U x Mi 


calories 


Heat absorbed by melted 
ice in warming to t m 


1 x Mi x (t — o) 


calories 


Latent heat of ice 


Li (calories per gram) 





90 LABORATORY EXERCISES IN PHYSICS 

Heat Equation. — Equate the total quantity of heat 
absorbed with the total quantity given out. (Why?) 
Solve for L^ the latent heat of ice, which is the only 
unknown quantity. 

If the calorimeter changes temperature, the quantity of heat 
lost or gained by it should be properly placed in the equation ; 
thus, if its temperature was higher than that of the mixture, the 
calorimeter lost heat, and the amount lost should be added to 
that lost by the water. 

Sources of Error. — (a) State the kinds of errors 
to which this experiment is liable in common with 
the preceding one. 

(5) What additional error may arise from wetness 
of the ice ? 

(e) If the ice or snow is collected from out doors 
when the atmospheric temperature is considerably 
below freezing, what source of error is present ? 
How may this further error be corrected or elimi- 
nated? 

Lessons. — The exercise affords practice in the 
manipulations of heat measurement, and in the 
principles and methods employed in solving prob- 
lems pertaining to heat transferences when the latent 
heat of melting is involved. 

Large quantities of heat (molecular kinetic energy) must 
be transformed into molecular potential energy in order that 
ice may be melted. The reverse transformation occurs when- 
ever water freezes. Try to explain in detail the applications of 
these facts to refrigerators and ice-cream freezers, and to the 
prevention of sudden changes of temperature in the vicinity of 
lakes. Try also to think out how the first fact operates to 
reduce the severity of spring freshets in ice-bound streams.- 



HEAT 



91 



Exercise Number 19 



LATENT HEAT OP VAPORIZATION 





References 


A 246 


GP 250 


C250 


GE 149-151 


C & C 335, 342 


H 285, 286 



H & W 213, 218 
J 54-55 
S126. 



Purpose. — It is proposed to determine the latent 
heat of vaporization of water. 

Apparatus. — (a) The boiler used in the last three 
exercises is to be furnished with a water-trap and 
delivery tube, 
as shown, and 
18 inches of 
rubber gas tub- 
ing for con- 
necting them 
with the boiler. 
All should be 

o y ' Fig. 19. — Calorimeter, cover, and water-trap : 

SO that Steam D, delivery tube ; T, water-trap ; C, rubber tube 

can escape from leading from boiler ' 

the boiler only through the end of the delivery tube. 

(J) A thick band of paper, or a wooden tube 
holder, is necessary for handling the hot apparatus. 

(c) Two thermometers, balance, weights, and pin- 
cers are to be near at hand. 

Operations. — (a) Half fill the boiler with water, 
generate steam, and take its temperature as in Exer- 
cise 16. 




92 LABORATORY EXERCISES IN PHYSICS 

(6) Remove the thermometer, and lay it in a safe 
and convenient place. With the holder, remove the 
tall tubular cover from the boiler, and screw on the 
flat cap.* 

(c) See that the trap and delivery tube are emptied 
of water, and connect them with the outlet tube of 
the boiler. 

(c?) Weigh the calorimeter, and having added 
about 200 cc. of water, weigh again. These weigh- 
ings should be made while waiting for the water to 
boil. 

(e) Take the temperature of the water, which 
should be at least 10° below that of the room. (If 
necessary, cool it with bits of ice before weighing. 
No ice, however, should remain unmelted at the time of 
recording the temperature.) 

(/) Immediately after taking the temperature of 
the water, introduce the delivery pipe through the 
perforated cover, and allow steam to pass vigorously 
through the water. A thermometer (better pre- 
viously warmed in the hand to about 10° above the 
temperature of the room) should be inserted through 
a second hole in the cover. 

(gr) Move the delivery tube about in the water, 
but do not place it so far below the surface that 
you cannot plainly hear the rattling of the collaps- 
ing steam bubbles. 

(K) When the temperature of the mixture is as 
far above that of the room as the water temperature 

* If the conical topped form is used, the openings should be 
closed with stoppers. 



HEAT 93 

was below it, note the temperature of the mixture, 
and at the same instant withdraw the delivery tube 
and also the thermometer. 

(i) Weigh the calorimeter with its contents, and 
from the three weights now recorded deduce the 
mass of the original water and also that of the con- 
densed steam. 

(j) If time permits, read the barometer and attached ther- 
mometer ; correct the barometer reading for temperature as in 
Exercise 16, and calculate the temperature of the steam by adding 
to 100° .037° for every millimeter by which the barometer col- 
umn stands above 760 mm., or subtracting .037° for every mil- 
limeter by which the barometer column stands below 760 mm. 
The boiling point thus calculated is likely to be more nearly 
correct than that taken by the thermometer. 

Data. — Enter all the observations as soon as they 
are taken, in a ruled tabular form like that on the 
next page. 

Heat Equation. — Equate the sum of the quan- 
tities of heat absorbed by the water and the calo- 
rimeter, with the sum of the quantities given 
out by the steam in condensing and by the re- 
sulting water in cooling to t° ; and solve for L s , 
the latent heat of steam, which is the only unknown 
quantity. 

Sources of Error. — (a) State those pertaining to 
each kind of observation, and to radiation and con- 
duction. Explain how they are provided against by 
the methods adopted. 

(5) Against what very important error dose the 
water trap provide ? 



94 LABORATORY EXERCISES IN PHYSICS 



Numerical Data 



Temperature of the water 


t w 


°C. 


Temperature of the mixture 


t 


°c. 


Temperature range of water 


t-t w 


°c. 


Mass of calorimeter and 
water 




g- 


Mass of calorimeter 




g- 


Mass of water 


M w 


g- 


Quantity of heat absorbed 
by water 


lxil/ w x (t-t w ) 


calories 


Quantity of heat absorbed 
by calorimeter 


MxM c x(t-t w )xi 


calories 


Mass of calorimeter, water, 
and condensed steam 




g- 


Mass of calorimeter and 
water 




g- 


Mass of condensed steam 


M s 


g- 


Quantity of heat yielded by 
steam while condensing 


L s x M 8 


calories 


Temperature of the steam, 
i.e. boiling point 


t s 


°C. 


Temperature range of con- 
densed steam 


t s -t 


°C. 


Quantity of heat yielded by 
condensed steam in cooling 


i x (t-;o x M a 


calories 


Latent heat of steam 


L 8 


calories 
per gram 



HEAT 95 

Lessons. — These are similar to those derived from 
the two preceding exercises. The student should 
state them concisely. 

What fundamental principle of Physics is as- 
sumed in the heat equations of Exercises 17, 18, 
and 19? 

Try to think out the applications of the high 
latent heat of vaporization of water and other 
liquids in the following cases : steam-heating ap- 
paratus, effect of evaporation and condensation in 
modifying atmospheric temperature, prevention of 
too rapid evaporation and condensation of moisture 
in nature, severity of burns caused by steam, loss of 
energy in a non-condensing steam engine, effect of 
moist winds in the distribution of atmospheric tem- 
perature, porous water-coolers, cooling effect of bay 
rum, relief from excessive bodily heat by perspira- 
tion and fanning, ice-machines, solidification of lique- 
fied gases by their own evaporation, the production 
of extreme low temperatures by the evaporation of 
liquid air. 



CHAPTER V 



MAGNETISM AND ELECTRICITY 

Exercise Number 20 
lines of magnetic force 



A 365-369 
C 256-268 
C & C 358-377 
S 221-225 



References 

GE 337-343 H & W 221-226 

GP 486-494 W & H 240-251 

H 291-301 JJ 68-87 

T 84-89, 119-121, 126-128, 142 



Purpose. — The purpose of this exercise is to de- 
termine the positions and directions of the lines of 
force in the magnetic fields of bar-magnets. 

Apparatus. — This 
consists of two bar- 
magnets, a box of fine 
iron filings, a sifter, 
a small compass, a 
board with grooves as 
shown, and a square 
of window-glass or 
glazed paper of the same size as the board. The 
sifter is either a square of fine wire gauze with its 
edges bent up, or a little bag of muslin. 

96 




Fig. 20. 



MAGNETISM AND ELECTRICITY 97 

Part A 

Operations and Observations. — (a) Place a magnet 
in one of the grooves and near the centre of the 
board. The flat surface of the magnet should not 
project above that of the board. Lay the glass or 
paper over the magnet and fasten it down with bits 
of soft wax or with thumb-tacks. 

(5) Determine the poles of the magnet. The 
north-seeking pole is that which repels the north- 
seeking pole of the compass-needle. (Why?) 

(e) Place some filings in the sifter, and by gently 
tapping it with a pencil sift the finest iron dust 
through it upon the glass (or paper), distributing 
them evenly, but not too thickly, all over the space 
around the magnet. 

(t?) Tap the board very lightly with the pencil or 
a ruler, using vertical blows only, and striking at 
different points successively until the filings have 
come into their positions of equilibrium in response 
to the resultant magnetic forces acting upon them in 
their respective parts of the field. 

(e) Now, upon the note-book page make a diagram 
of the magnet and the filings. The copy of the out- 
lines of the magnet, and of the curves into which 
the filings have settled in all parts of the field, 
should be as faithful as you can make it. If not of 
the same size, the proportions should be carefully 
preserved. Letter the poles iVand S. 

(/) Place the compass, successively, near each 
corner of the magnet, and also opposite the middle 



98 



LABORATORY EXERCISES IN PHYSICS 



of each end and of each side ; at each of these points 
observe the position into which the needle settles ; 
and at the corresponding position on the diagram 
draw a short arrow with its point in the position of 
the north-seeking pole of the needle. 

(#) Remembering that the lines represented by the 
filings are not broken, but continuous, draw several of 
these full lines on each side of the axis of the mag- 
net. Note that they are closed curves (but not circles 
or ellipses), each one passing out of the north-seek- 
ing pole of the magnet and around on the outside 
toward the south-seeking pole, then through the 
body of the magnet to the point where you began to 
trace it. Note also that the curves are bisymmetri- 
cal with respect to the axis of the magnet. 

(K) .Over the diagram write the heading, Field of 
a Single Bar Magnet ; and under it write, " Each 
line of force represents at any point the direction 
which a free north-seeking pole would take at that 
point in consequence of the resultant magnetic force." 



(a) Arrange the 



Part B 
magnets as 





1 









Fig. 21. 



shown in either 
diagram (Figure 
21), and repeat 
all the operations, 
again drawing ar- 
rows at the char- 
acteristic points 
of the field. 
(5) Above the 



MAGNETISM AND ELECTRICITY 99 

diagram write the heading, Field of Two Bar Mag- 
nets, Side by Side (or End to End), Like Poles 
Adjacent; and below the diagram state what the 
lines represent, as before. 

Part C 

(a) Place the magnets as in one of the diagrams 
of Figure 21, — the one not chosen in Part B, — but 
reverse one of the magnets so that unlike poles shall 
be adjacent. 

(J) Make all observations and records as in the 
preceding cases. 

Inferences and Lessons. — (a) Is the magnetic field 
confined to the plane of the board, or does it include 
all planes ? How can this be proved ? 

(5) In each case, where is the strength of field the 
greatest ? 

(e) Show by small diagrams the arrangement of 
the lines of force between two poles that are repelling 
each other and between two poles that are attracting 
each other, and label them appropriately. 

(cZ) In investigating magnetic properties and 
their consequences it is very important to know 
definitely the directions of the lines of force and the 
relative strengths of different parts of the field. 

Additional Work. — If there is time (a) place a small rect- 
angle of soft sheet-iron between the two poles in the arrange- 
ments of Parts B and C, and sketch the field, stating concisely 
what changes in the paths of the lines are due to the perme- 
ability of the soft iron. 

.ore. 



100 LABORATORY EXERCISES IN PHYSICS 

(b) Map the lines about a bar magnet pole in a plane per- 
pendicular to the axis of the magnet. 

(c) Map the field of a horseshoe magnet lying flat and also 
with poles up. 

(d) Very pretty results may be obtained by mapping the 
field of three or more magnets arranged in a triangle, square, 
pentagon, cross, etc. 

Permanent Maps. — If the student does something in photog- 
raphy, he will find it very fascinating to repeat these experi- 
ments in a dark room, using a photographic plate instead of 
the glass or paper. Make the map by ruby light on a slow 
or medium plate, exposing to the light of a match at one or 
two feet distance, then developing and fixing in the ordinary 
way. Developing or printing-out papers also give excellent re- 
sults. In all cases carefully avoid over-exposure. 

Another method is to coat a sheet of ordinary glass with 
shellac varnish; dry it; make the map; and then warm it on 
a sand-bath over a stove until the shellac softens and the filings 
sink into it. 

Maps made on glass, when backed with ground or opal 
glass and bound or framed for transparencies, will make pretty 
ornaments. 

Pieces of watchspring, straightened and magnetized, make 
excellent magnets for all these experiments, and cost nothing. 

Exercise Number 21 

field of electromagnetic force 

References 

A 375, 377, 381 GE 349-354, 308, 309 H & W 252 

C 269, 270, 291, 315, 317-319 GP 445, 507-514 JJ 119-126 

C&C452-459 H 371-376 S 226-228 

T 195-204, 389, 390, 393 W & H 278, 281-284 

Purpose. — It is proposed to investigate the 
magnetic field about a current-bearing conductor. 



MAGNETISM AND ELECTRICITY 101 

(a) When straight. (6) When in a single loop. 
(V) When in a helix. (d) When in a flat coil. 
(e) When the helix or coil is associated with a soft 
iron core. 

Apparatus. — The apparatus and its arrangement 
are shown in the diagram. A drawing made from 
the objects themselves should be placed in the note- 




Fig. 22. — Conductors arranged so that their fields of electromagnetic 
force can be mapped. 

book. Iron filings, sifter, and compass are provided 
as in Exercise 20 ; also a square and a rectangle of 
soft sheet-iron. 

Operations and Observations. — (a) Dip the bare 
wire, A, into the box of filings, and make a sketch of 
what you see. 

(6) Sift filings over the two boards, tap the boards 
till the filings find their places, disconnect the cur- 
rent and sketch the fields about B, (7, and D. If 
you are using the dynamo current in series with other 
tables, do not disconnect. The teacher will attend to 
that. 

(<?) Place the compass in the characteristic parts 
of each field, B, (7, D, and draw thin arrows in cor- 
responding positions in your diagrams just as in 
Exercise 20. 



102 LABOBATOBY EXEBCISES IN PHYSICS 

(cT) Place the rectangular strip of sheet iron 
lengthwise in the helix, (7, but not touching it, and 
similarly place the square in the flat circular coil, i), 
repeat operations (5) and (c), making new diagrams, 
or stating each effect in words, as preferred. 

(e) The direction of the current will be given you 
by the teacher. Indicate it by short, thick arrows in 
all parts of the circuit and especially near the coils. 

(/) Do not crowd the diagrams, nor make them 
too small. It is better to put only one drawing on a 
page. Label the fields, Straight Wire, Helix, etc. 

Inferences and Lessons. — Make clear, concise sen- 
tences answering the questions below. 

(a) What is the form of a line of force about A or B ? 

(5) Looking along the wire in each case with the 
direction of the current, do the lines of force go 
clockwise or counter-clockwise ? 

(<?) What is the direction of the lines of force if 
the current is coming toward you ? 

(d) Is the field of what it should be if the lines 
of force are the resultants of the lines of force of 
several loops like the single one B ? 

(e) Compare the fields of C and D with those 
which would belong to similarly shaped bar magnets. 

(/) How is the strength of field affected by using 
several loops in a compact coil instead of a single loop, 
provided the strength of the current is the same ? 

($0 What effects are due to the permeability of 
the soft iron cores ? 

What is the name given to a helix or flat coil hav- 
ing a soft iron core and carrying a current ? 



MAGNETISM AND ELECTRICITY 103 

Qi) What can you infer as to the behavior of all 
such coils and helixes toward each other and toward 
magnets ? Try to find applications of electromagnets. 

Note. — The upper surfaces of the boards are very smooth 
and painted white or else covered with white glazed paper which 
was glued on before drilling the holes. The binding posts may 
be omitted and their places taken by double connectors. The 
wire of A , B, and C, is No. 16 bare copper; of Z), No. 16 cotton- 
covered magnet wire. The required current is best furnished 
by a direct current dynamo or storage battery, all the apparatus 
in the laboratory being joined up in series. In this case the 
teacher will regulate the current by means of a suitable resist- 
ance, and inspect the connections before turning on the current. 

In case the school is not provided with a dynamo and the 
tables are not wired, one or two chromic acid cells are to be 
connected in series with each apparatus. 

Exercise Number 22 
study of a simple voltaic cell 

References 

A 346-319, 385-385 d H 346-355 

C 294-297 H & W 243-246 

C & C 428-442 JJ 30-36, 40-44, 47-55 

GE 297-304, 308, 309 S 231, 234, 240 

GP 429-441, 467 W & H 269-271, 274-277 

Purpose. — The purpose of this exercise is to in- 
vestigate the action of a simple voltaic cell. 

Apparatus. — The apparatus and materials consist 
of a battery jar, nearly full of dilute sulphuric acid 
(1 part acid to 20 parts water), two zinc plates, one 
of them amalgamated with mercury, a copper plate, 



104 LABORATORY EXERCISES IN PHYSICS 



a wooden cleat with 




Fig. 23. — Showing method of sup- 
porting and connecting the plates. 



two saw cuts in which to 
support the plates, a 
compass, and a double 
connector. 

Preliminary Direc- 
tions. — (a) Caution ! 
Throughout the experi- 
ment the jars and plates 
should be kept in a tray 
of sheet lead provided 
for the purpose. The 
acid is very destruc- 
tive, and under no cir- 
cumstances should it 
be allowed to drip on 
the table or clothing. 
Should such an acci- 
dent occur, quickly wash 
away the acid with a 
weak ammonia solution, 



followed by plenty of water. 

(5) Do not inhale the unpleasant fumes. 

(tf) Do not allow the amalgamated zinc to touch 
either of the other plates. 

(cT) In describing the apparatus, make a diagram 
showing (1) cell with plates and liquid in position, 
wires joined, and compass needle in the observed 
attitude; (2) plates, marked respectively Cu (cop- 
per) and Zn (zinc); (3) electrodes, marked respec- 
tively + electrode and — electrode ; (4) solution, 
marked sulphuric acid. 



MAGNETISM AND ELECTBIC1TY 105 

(e) After each observation, remove the plates 
promptly (to a jar of water, which should stand 
ready in the tray). 

(/) Before beginning each operation, see that the 
liquid has cleared of bubbles previously formed. 

Operations. — (a) Place the copper strip in the acid. 
Is any chemical action indicated by gas bubbles rising 
from the plate ? 

(5) By means of the cleat, support the copper and 
the unamalgamated zinc side by side in the acid, not 
allowing either the plates or their wire terminals to 
touch each other. Is there now any chemical action ? 
If so, from which plate do the bubbles come ? Note, 
as well as you can, the rapiditj^ of the action, so as to 
compare it with that in other cases. 

(e) By means of a double connector, join the wire 
that leads from the copper (i.e. the + electrode) to 
the wire that leads from the zinc (i.e. the — elec- 
trode). Do bubbles rise from either or both plates ? 
If from both, from which plate do the most bubbles 
come off ? Is the action more vigorous than in 
Case (J) ? 

(oT) Pass the wire in a north-south direction over 
the compass needle. Is the needle deflected? As 
you look along the wire, does the north- seeking pole 
move in the clockwise or counter-clockwise direction 
with regard to the wire ? Then, remembering the 
relation of lines of force to current which you 
learned in the preceding exercise, state whether the 
current passes along the wire from copper to zinc, or 
in the reverse direction. 



106 LABORATORY EXERCISES IN PHYSICS 

(#) Replace the unamalgamated zinc by the amal- 
gamated, leaving the circuit open ; and compare the 
observations with those of Case (J). Record the 
result. 

(/) Join the electrodes. Where do the bubbles 
originate now ? Compare the vigor of the action 
with that in Case (<?). Record the result. 

(#) Pass the wire over the compass, as in Case (c?). 
Is the direction of the current the same ? Is the 
strength of the current greater (indicated by a 
greater deflection) ? 

(A) Compare the two zincs, and (if possible) note 
which has wasted the most by the chemical action. 
(The only certain way is to expose them equally and 
weigh each before and after.) Does the copper show 
any signs of wasting ? 

(i) Note whether any heat energy has developed, 
as indicated by plates or liquids becoming warmer. 

Carefully space your notes, writing them in columns 
headed Operations, Observations, Inferences, so that 
each operation and its corresponding observations and 
conclusions shall stand out prominently on the page. 

Lessons. — (<x) Energy changes. 1. If the elec- 
trodes are tested on open circuit by means of a very 
sensitive electroscope (or electrometer), the + elec- 
trode shows a positive electrostatic charge and the 
— electrode a negative charge. Chemical potential 
energy of zinc and acid has been transformed into 
electrical potential energy. 

2. When the circuit is closed, this is transformed 
into electrokinetic energy, associated with the con- 



MAGNETISM AND ELECTBICITY 107 

ducting wire. 3. This energy can do several kinds 
of work. (What kinds ?) The supply of energy is 
kept up at the expense of zinc and acid as long as 
the circuit remains closed, or until the chemical 
potential energy is exhausted. 

(5) Since the zinc wastes away, and the copper 
does not, it is evident that the chemical change takes 
place at the zinc plate and not at the copper. But 
the hydrogen bubbles originate at the copper plate. 
Therefore we conclude that the chemical action is 
handed along from molecule to molecule through the 
liquid. 

(e) Amalgamating the zinc largely prevents "local 
action," due to iron or carbon particles existing as 
impurities in the commercial zinc. By local action 
chemical energy is transformed into heat in the cell 
and is wasted, instead of being wholly transformed 
into electrokinetic energy, available in the external 
circuit. 

GALVANOMETERS 

References 

A 414-444 I GE 321-323. 332 H & W 252 

C 291, 318 GP 465-468, 479 JJ 144-154 

C & C 471-474 H 382-386, 393 S 230 
T 208-221 W & H 278-280 

Galvanometers should be secured to a solid wall, 
or be placed on a shelf supported by the wall, and 
not connected in any way with the floor. If set up 
on a table, the table must be as free as possible from 



108 LABORATORY EXERCISES IN PHYSICS 

any tendency to jarring or vibration. It is necessary 
that a good light shall fall on the scale. 

Caution. — Do not attempt to make any of the 
galvanometer adjustments until the instructor has 
personally directed you. Such further instructions 
as are thought proper will be supplied. The adjust- 
ments described in the sentences marked thus, *, are 
rather difficult, and in attempting them without per- 
sonal direction the inexperienced person is likely to 
disable the instrument. 

D'Arsonval Galvanometer. — To adjust the D'Ar- 
sonval galvanometer, it must first be levelled by turn- 
ing the levelling screws at the base, so that the coil 



| SUSPENSION 
TUBE 

T£LESCOPE 



CO/L- 



Ma cnets 




IEVEUNG ^SCREWS 

Fig. 24. — D'Arsonval Galvanometer. 



MAGNETISM AND ELECTRICITY 109 

can turn freely without touching either the magnets 
which embrace it or the core which it surrounds. 
The weight of the coil may be lifted off the suspen- 
sion by a screw or lever, which acts upon it from 
behind. To lower the coil into its position for use, 
turn the screw or lever until the coil hangs freely by 
the suspension. *The adjustment of the coil to the 
correct height is made by raising or lowering the 
short rod or pin to which the suspension is attached. 
This pin is supported by a little collar at the top of 
the instrument, and is held at the proper height by a 
set screw. 

* By loosening a set screw in the support or suspen- 
sion tube, this collar can be rotated so as to bring the 
plane of the coil into the plane of the magnet poles. 

If necessary, the levelling screws are again to be 
adjusted. 

The indications of the instrument are read by a 
pointer, which swings over a scale, or by a mir.ror, in 
which a reflected image of the scale is viewed through 
a telescope provided with a vertical cross-hair. In 
the latter case the eyepiece of the telescope is fo- 
cussed so that the cross-hair appears distinct. The 
telescope and scale are placed directly in front of the 
mirror, the one a little above, and the other an equal 
distance below the level of the centre of the mirror. 
The image of the scale appears in the field of view of 
the telescope, and if the image of the scale is not 
clear, the telescope must be carefully focussed by 
means of the draw-tube. Finally,* the telescope, the 
scale, or the coil (depending on the make of instru- 



110 LABORATORY EXERCISES IN PHYSICS 



ment) is swung a very little to the right or left until 
the cross-hair coincides with the zero of the scale. 

The D'Arsonval shown in Fig. 25 is read as fol- 
lows : Place the eye just behind the scale, looking 
either through the peephole or a very little to one 




Fig. 25. — D'Arsonval Galvanometer, with sight and scale attachment. 

side of it, and just, on a level with the top edge of 
the scale. You will see a reflection of the scale in 
the suspension mirror. Also, above this image of the 
scale there will appear in the silvered upper half of 
the cover glass the reflection of a vertical reference 
mark that is placed above the scale. When the in- 



MAGNETISM AXD ELECTRICITY 



111 



strument is levelled and the coil lowered as mentioned 
above, the zero of the scale image will nearly coin- 
cide with the reference mark image. If it does not, 
the cover tube of the mirror-box is to be revolved 
a very little to the right or left, until the correct 
adjustment is secured. 

Astatic Galvanometer. — This instrument must be 
set so that the axis of its coil 
extends east and west (or, 
in other words, so that the 
plane of the coil is north and 
south). The instrument is 
then levelled, and the needle 
adjusted to swing freely 
within the coil. These ad- 
justments are similar to those 
described for the D'Arson- 
val. The needle, if properly 
freed from torsion and fric- 
tion, will lie in a definite 
position ; and the zero of the scale should be brought 
directly under the pointer. 

Tangent Galvanometer. — This galvanometer, like 
the others, is levelled at the base ; but since the 
pointer is set at right angles to the needle, the diam- 
eter through the two zero marks of the scale must lie 
east and west, and the plane of the coil must be in 
that of the magnetic meridian. If there is a lever or 
screw to lift the needle when not in use, the needle 
must be lowered by means of it until it swings freely 
on its pivot. The instrument is then rotated until 




Fig. 26. — Astatic Galvano- 
meter. 



112 LABORATORY EXERCISES IN PHYSICS 




Fig. 27. — Tangent Gal- 
vanometer. 



the zero marks are exactly under the ends of the 
pointer. 

In order to be adapted to cur- 
rents of different strengths, tan- 
gent galvanometers frequently 
have two or more coils on the 
same reel. If there are three 
coils, there will be four binding- 
posts. If the two posts at the 
left are connected with the cir- 
cuit, the first coil only is placed 
in circuit. The two at the right 
throw in the third coil only, the 
two at the middle the second 

coil only. The first and third posts throw in the first 

two coils, the second and fourth posts the last two 

coils, and the first and fourth posts all three coils. 
Usually, the connections are so chosen as to give 

the needle a deflection of about 45°, because with that 

reading the errors are 

smaller in proportion than 

for either larger or smaller 

deflections. 

COMMUTATOR 



In many experiments it 
is necessary that the cur- 
rent passing through the 
galvanometer be quickly 
reversed. Accordingly, a 
commutator, or reversing 




Fig. 28. — Commutator. The 
wires leading from the galva- 
nometer are inserted at posts GG, 
and those leading from the cur- 
rent circuit at posts CO, 



MAGNETISM AND ELECTRICITY 



113 



switch, is provided. A convenient and inexpensive 
device is shown in Fig. 28. 

The connections are made as shown, by wires dip- 
ping into holes containing mercury. To reverse the 
current through the galvanometer, lift the top, turn 
it through a right angle, and replace it. To break 
the current, simply leave off the cover. 

SHUNTS 

A strong current should never be sent through a 
sensitive galvanometer. In beginning an experiment, 
it is always best to shunt the galvanometer by con- 
necting its two binding-posts across by means of a 
short wire, so that only a small fraction of the current 
goes through it. When the current is so small that 
the galvanometer is insensitive, a shunt of higher re- 
sistance may be used, or the shunt may be discarded. 



MICROMETER SCREW CALIPER 

In one kind of micrometer caliper, the pitch of the 
screw (distance between two adjacent threads, meas- 
ured parallel to the axis) is 1 mm. ; and the cir- 
cumference of the head is 
divided by a circular scale 
into one hundred equal 
parts. In another kind, 
the pitch is \ mm. ; and the 
circular scale has fifty equal 

•ppp-^g Fig. 29. — Micrometer Caliper. 

* ' Pitch \ mm. Circular scale in 

When the end of the 50 equal parts. 




114 LABORATORY EXERCISES IN PHYSICS 

screw rests against the stop, B (without strain), the 
edge of the circular scale should coincide with the 
zero mark of the linear scale, a ; and the zero line of 
the circular sca]e should exactly coincide with the 
horizontal reference line. 

It should be noticed that in the first kind of mi- 
crometer caliper, the zero mark of the circular scale is 
identical with the .100 mark ; and in the second kind 
it is identical with the .50 mark. 

In the first kind of micrometer caliper, if the head 
of the screw is given one complete turn toward you, 
the screw end retires from the stop to a distance 
equal to the pitch of the screw (1 mm.) ; and the 
edge of the circular scale will coincide with the divi- 
sion 1 on the linear scale, which therefore denotes 
the distance in millimeters between the screw end 
and the stop. Also, the zero mark of the circular 
scale will again coincide with the reference mark. 
Now if the head be turned farther around till the 
division numbered 25 coincides with the reference 
line, the screw has retired from the stop a further 
distance equal to twenty-five hundredths of the pitch 
of the screw (i.e. .25 mm.). Similarly, if the screw 
has been turned so that the linear scale shows seven 
and a fraction of its millimeter spaces, and the 69th 
division of the circular scale coincides with the refer- 
ence line, it is clear that the screw has turned through 
seven and sixty-nine hundredths revolutions, and 
the screw end is distant from the stop just 7.69 mm. 

To Measure the Diameter of a Wire. — (a) With- 
draw the screw from the stop and place a straight 



MAGNETISM AND ELECTRICITY 115 

portion of the wire between them, so that it lies fiat 
against the face of the stop. Turn the head till the 
face of the screw end rests against the wire firmly 
enough so that you c&n just feel the resistance. 

(6) To read the First Kind of Caliper. — With the 
line of sight perpendicular to the scales at the refer- 
ence line, read the number of whole millimeters on 
the linear scale, and the number of tenths and hun- 
dredths of millimeters on the circular scale. 

(c) Determine the zero error by setting the screw 
end gently against the stop, and observing the scale 
readings as before. If the zero of the circular scale 
coincides with the reference line, no correction is 
required. If there is a small negative reading, it must 
be added to all readings of the caliper ; and if there 
is a small positive reading, it must be subtracted. 
(Why ?) 

(cZ) To read the Second Kind of Caliper. — In this 
case also, each division of the circular scale corre- 
sponds to one-hundredth of a millimeter (because -^ 
of J mm. = yl-Q mm.). Read the number of whole 
millimeters on the linear scale, and add the hun- 
dredths indicated on the circular scale just as directed 
above ; but if the fractional part of a millimeter ex- 
posed on the linear scale is greater than one-half then 
.50 must be added to the reading, in order to state 
correctly the fractional part. (Why ?) 

Thus, in Fig. 29, the caliper reads 1.50 mm. If D 
were turned so as to bring C nearer to B by -^ of a 
revolution, the reading would be 4.45 mm. ; but if 
D were turned so as to withdraw C by |-| of a 



116 LABORATORY EXERCISES IN PHYSICS 

• 
revolution, the corresponding reading would be 
4.23 + .50 =4. 73 mm. 

(e) Several measurements should always be taken 
along different parts of the sample of wire. (Why?) 

(/) Micrometers measuring in inches usually have 
a linear scale with units ^ of an inch in length, and 
the circular scale divided into 40 equal parts. What 
fraction of an inch does one division of the circular 
scale measure? 

(#) If the head of the screw is fairly large, it is 
easy to estimate tenths of the divisions of the circu- 
lar scale and thus estimate thousandths of millimeters, 
or ten-thousandths of inches. 



Exercise Number 23 
electrical resistance 

References 

A 350-353, 414-416 JJ 95, 98, 99-101, 106, 107, 151, 
C 312, 324 152, 154, 160-168 

C & C 460-463, 471, 473, 475, H 377-380, 383-389 

479 H & W 256 

GP 455, 470-473, 479 S 230, 234, 235 

GE 315, 324-328 W & H 279-280, 290-294 

Purpose. — The purpose of this exercise is to meas- 
ure the electrical resistances of wires of various 
dimensions and materials, to verify the laws that 
state the relations of resistance to length, sectional 
area, and substance, and to determine the resistivities 
of the materials of which the wires are made. 



MAGNETISM AND ELECTRICITY 



117 



Method. — The resistances are to be measured by 
the method of Wheatstone's Bridge. 

Theory of the Wheatstone Bridge. — Let there be 
an arrangement of conductors forming a divided cir- 
cuit as represented 
in the diagram. 

Let a current 
from the battery 
divide at A into 
two branches, and 
reunite at D ; and 
let the point be 
so chosen with 
reference to B that 
no current passes 




Fig. 30. 



-Explaining the theory of Wheat- 
stone's Bridge. 



through a galvanometer, 6r, in connection with these 
two points. Then B and are equipotential points. 
(Why ?) Also, — 

let F x and r x be the fall of potential and the resistance 
between A and B, 
F 2 and r 2 be the fall of potential and the resistance 

between B and D, 
F s and r 3 be the fall of potential and the resistance 

between A and (7, 
F± and r 4 be the fall of potential and the resistance 
between C and D. 
Then F 1 = F s (being the falls of potential from A to 

the equipotential points B and (7), 
and F 2 = F± (being the falls of potential from the 
equipotential points B and C to 2)). 



118 LABORATORY EXERCISES IN PHYSICS 

■•■f* = fj. (Why?) 

But 5 = ^ and § = ^- 

-^2 »2 ^4 »4 

(The fall of potential along any part of a conduc- 
tor is proportional to the resistance of that part.) 

r. To 



11 = 13 



(Why?) 



Corollary. — Since the resistances of conductors 
of uniform material and sectional area are propor- 
tional to their lengths, it follows that if ACD be a 
wire of uniform material and thickness, the ratio of 

the lengths of the segments A and CD ( i.e. — 3 j, may 
be substituted for the ratio of their resistances ( ^ ) an( j 



r L * . 

we shall have - 1 = — %. If three of the quantities in 

either of the above proportions are known (or can be 
measured), the fourth can be calculated. 

Apparatus. — The apparatus consists of a D'Ar- 
sonval or an astatic galvanometer ((?), of a Wheat- 




Fig. 31a.— Wheatstone's Slide-wire Bridge. 



stone slide-wire bridge, shown in Fig. 31 a and b ; 
one or two cells of battery Ba, in series ; the wires 



MAGNETISM AND ELECTRICITY 



119 



whose resistances and dimensions are to be deter- 
mined, and a known resistance, to be used as a stand- 
ard. Two pairs of thick short wires or copper strips 
of equal dimensions are provided for connecting in the 
known and the unknown resistances ; and two pairs 
of long leading wires are also to be used for connect- 

Ba 

Key 




L 3 L 4 

Fig. 316. — Simple form of Slide-wire Bridge, showing connections. 

ing the battery and the galvanometer with the bridge. 
The resistances of the heavy copper conductors are 
negligible, except where extreme accuracy is sought. 
The wire is of uniform sectional area, just a meter 
long,* and stretched over a meter rule. It is made of 
an alloy (German silver, or better, platinoid), hav- 
ing a resistance that is relatively high and that 
changes little on account of ordinary temperature 
changes. Make a diagram or sketch of the apparatus 
when connected. 

Part A 

TO MEASURE RESISTANCE 

Operations. — (a) By means of the binding-posts 
make the connections as indicated in the diagram 

* In some bridges the wire is a half-meter long. 



120 LABORATORY EXERCISES IN PHYSICS 

above. r x is the known resistance, and r 2 the un- 
known, or vice versa. See that all binding-post con- 
tacts are scraped clean and bright and are firmly set. 

(6) Slide the contact piece along the wire until a 
point O is found, such that when contact is made 
there the galvanometer needle shows no disturbance. 
Do not scrape the wire. (Why ?) 

(e) Test the adjustment by seeing if equal and 
opposite deflections are caused by making contact at 
a very short distance on the right of this point, and 
then at the same distance on the left of it« If neces- 
sary, readjust till the point is found which satisfies 
this condition. 

(c?) Read and record in millimeters the lengths 
L s and £ 4 of the segments into which divides 
the wire. 

(e) From the corollary to the general theory al- 
ready given, in connection with an inspection of the 

r L 

diagram above, it is plain that - 1 = — 3 . Substitute 

the values of the three known quantities and solve 
for the unknown resistance. 

(/) Now interchange the known and the unknown 
resistances, repeat the operations, solve the equation 
for the new value of the unknown resistance, and 
take as the true value the mean of the two deter- 
minations. 

Remarks. — In making the preliminary trials for 
finding the point (7, have the galvanometer shunted. 
Make contact at distances of 10 cm. along the wire, 
beginning at the left end, until the galvanometer re- 



MAGNETISM AND ELECTRICITY 



121 



verses its deflection ; then go backward, toward the 
left end, making contact at distances of 1 cm. When 
the point is located within 1 cm., make contact 
by steps of 1 mm. Avoid any cause for heating the 
wire. (Why ?) 

It is well to place a key in the battery circuit, and 
to close this circuit just a little before making con- 
tact on the wire, leaving the battery circuit open at all 
other times. (Why ?) 

Part B 

To verify the law of the relation of resistances to 
lengths, the sectional areas being equal and the tem- 
perature constant. 

Operations and Data. — Qa) On the resistance rack 
(Fig. 32) are 200 cm. of No. 28 German silver wire 
between the binding-posts A and B. (The resist- 
ance of the copper washer, i", may be neglected.) By 



::■ 



_z^_ 



Fig. 32. — Resistance Rack. 



B 



means of the short, thick conductors provided, con- 
nect the posts at A and B with the posts at one of 
the openings of the bridge, and in like manner con- 
nect the terminals of a known resistance to the posts 
at the other opening. 



122 LABORATORY EXERCISES IJST PHYSICS 

(5) In accordance with the directions in Part A, 
determine the resistance of the German silver wire 
(on both sides of the bridge), and set out the values 
and their mean at the right of the calculation and 
near the margin of the page, so that they may be 
conspicuous. Also place their average beneath them. 

(V) By means of binding-posts B and 2), connect 
the 400 cm. of wire, and repeat the operations. 

(rf) Similarly measure the resistance of the 600 
cm. between A and D. 

(#) On a single page by itself rule a tabular form 
in which all the data of the exercise are to be 
entered. Head the page, Data, Exercise 23. 

Place the following headings in a vertical column : 
Substance ; B. & S. Gauge Number ; I — length (cm.); 
Diameter (mm.); Radius (mm.); r = radius (cm.); 

a = Area = 7r 2 r (sq. cm.); R = resistance (ohms.); 

7? 7? 

Ratio, — - (ohms per cm.); Ratio, — ; Resistivity, 

K= R~. , To the right of this column make a ver- 
tical column for each wire, and in it enter, when 
obtained, the data for that wire, opposite its proper 
heading. 

Calculate the ratio, — (ohms per centimeter), for 
t 

each of the three wires, and enter it in its appropri- 
ate place. It should be expressed as a decimal fraction. 
Inferences. — (a) Choosing suitable scales for the 
values of R and Z, and using the latter as abscissas 
and the former as ordinates, plot a " curve " showing 
the relation of resistance to length. Does the curve 



MAGNETISM AND ELECTRICITY 



123 



If so, what relation 



approach to a straight line ? 
may be inferred ? 

(5) Are the values of — - for the three different 

V 

lengths of No. 28 German silver wire nearly enough 
equal so that the differences may be ascribed 
to the errors of experiment? If so, may we write 

— 1 = —^ = — B = a constant ? 

n ^2 ^3 

(<?) Give the formal statement of the law verified. 

Part C 

To verify the law of the relation of resistance to 
sectional area, the substance, length, and temperature 
remaining the same. 

Operations and Data. — (a) As in Part B, measure 
the resistance of the 600 cm. of No. 18 German sil- 
ver wire between binding-posts E and F of the resist- 
ance rack.* 

(5) Measure the diam- 
eters of each of the two 
sizes of German silver wire 
at several points, and if 
they vary, take the average 
for each size. Do not meas- 
ure them on the rack unless 
told to do so by the instruc- 
tor, as careless handling Fig. 33. — B and S Wire Gauge. 

* The illustration (Fig. 32) represents only 200 cm. It is 
better to have 600 cm. of each of the other wires arranged like 
the first wire. The intermediate binding-posts are not necessary 
for these, however. 




124 LABOBATORY EXEBCISES IN PHYSICS 

may stretch or displace the Avires. Use samples of 
the same wires provided for the purpose. By means 
of the B. & S. wire gauge (Fig. 33), verify the 
gauge number of each wire. The correct number 
is the one opposite that slot into which a straight 
portion of the wire will just fit without bruising. 
The gauge number being ascertained, the correspond- 
ing diameter may be taken from a table of gauge 
numbers and diameters. A better way to determine 
the diameter of the wire is to measure it with the 
micrometer screw caliper as directed on p. 115. 

(e) Calculate the ratio, — , for each of the two sizes 
p . a 

oi wire. 

(c?) Enter in tabular form all the additional data 

obtained in this part. 

Inferences. — (a) Are the two values of — nearly 

a 

enough equal so that you may ascribe the difference 
to experimental errors ? If so, what proportion 
may you write ? 

(6) State the law verified. 

Part D 

To determine the resistivities of wires of different 
materials and learn whether the substance of a wire 
affects its resistance. 

Operations, Data, Calculations. — (a) Measure pre- 
cisely as before the resistance of the 600 cm. of No. 28 
copper wire between posts Gr and H, 

(6) Obtain its diameter as in Part C. 



MAGNETISM AND ELECTBICITY 125 

(<?) Having reduced the lengths and sectional 
areas of all the wires measured in the exercise to 
centimeters and square centimeters, calculate the re- 
sistivity of each wire in turn. To do this, substitute 

in the formula, K= R -, where if is the resistivity, R 

the resistance, a the sectional area in square centim- 
eters, and I the length in centimeters. It represents 
the resistance in ohms per centimeter of a conductor 
one square centimeter in cross-sectional area. 

(c?) Enter all the remaining data in the tabular 
form. 

Inferences. — (a) If the first two laws are true, 
how should the values of the resistivity of German 
silver obtained from the different samples of German 
silver wire compare with each other ? 

(6) Are the differences small enough to be ascribed 
to experimental errors ? If there are large differ- 
ences, they may be due to mistakes in calculation 
(look for them), or possibly to actual difference in 
composition of the different specimens of wire, or to 
variations in the temperatures at which the measure- 
ments were made. 

(e) Compare the mean resistivity of the German 
silver with that of the copper by dividing the former 
by the latter. What is the ratio ? 

(c?) State the law which is verified by the com- 
parison made in (V). (Obviously a similar compari- 
son can be made by dividing the resistance of the 
No. 24 German silver wire by the resistance of 
the No. 24 copper wire.) 



126 LABORATORY EXERCISES IN PHYSICS 

Sources of Error. — State briefly the most obvious 
sources of error in the different operations of this 
exercise. 

Exercise Number 24 

measurement of current strength 

References 

A 357, 358, 414, 429-431 H & W 251, 254, 255 

C & C 445-451, 464, 472 JJ 59-67, 96, 145, 153, 155-159, 

C 298, 307-309, 324 370-383 

GP 442-444, 451, 452, 463-467, S 230, 236, 237 

548 T 162, 178, 190, 212, 236-245, 
GE 307, 313, 322, 332 492-496 a 

H 365-369, 382, 393 W & II 279-280, 290-294 

Purpose. — The purpose of this exercise is to meas- 
ure the strength of an electric current by means of a 
gas voltameter, and to determine the constant of a 
tangent galvanometer. 

Apparatus. — (a) The voltameter consists of a gas 
measuring tube, graduated in cubic centimeters, and 
a glass vessel containing dilute sulphuric acid, into 
which are inserted two electrodes of platinum or 
lead (Fig. 34 a). 

(5) The galvanometer, a commutator (Fig. 28), 
and the voltameter are connected with the lead- 
ing wires from the source of current, as shown 
(Fig. 34). To avoid spilling the acid, the voltam- 
eter should be placed in a leaden tray. 

(<?) A thermometer is suspended near the tube. 

(c?) For measuring the time, the seconds clock, or 
stop-watch, or an ordinary watch is needed. If a 



MAGNETISM AND ELECTRICITY 



127 



mm 



®=f 



Fig. 34. — Connec- 
tions for current meas- 
urement: Ba, battery; 
V, voltameter; C, com- 
mutator ; G, galvanome- 
ter ; RB, resistance box. 



watch is used, see that the minute hand and second 

hand are so set as to begin each 

minute simultaneously. 

Operations. — (a) See that the 

galvanometer is properly levelled 

and set at zero, and that the con- 
nections are properly made, with 

the circuit closed except at one 

single point (at the dynamo switch, 
or, if the inde- 
pendent battery 
current is used, 
at the commu- 
tator. 

(6) Make sure 
that the elec- 
trode over 
which the tube 
is to be placed 
is the cathode, 
and that it is 

standing vertically upward, so that 

the tube can go neatly over it. 
(e) From a beaker pour some of 

the dilute acid into the tube until 

it is nearly filled (within two or 

three cubic centimeters) ; close the 

end with the thumb. Cautiously 

J Fig. 34 a.— GasVol- 

mvertmg the tube, place its end tameter, supported 
under the surface of the acid in the by a rill * r and clam P- 
jar, and remove the thumb. Keeping the open end 



128 LABORATORY EXERCISES IN PHYSICS 

of the tube beneath the surface of the acid, place it 
over the cathode, and support it in a vertical position 
by means of a screw clamp and support rod. Be 
careful not to touch the upper part of the tube with 
the hand. (Why ?) 

(cT) Read the number of cubic centimeters of gas 
in the tube, estimating tenths of the smallest scale 
divisions. Read from the bottom of the meniscus. 
Observe the temperature. [It should be kept con- 
stant, if possible, throughout the experiment. The 
temperature of the acid should be the same as that 
of the room.] 

(e) All being now in readiness for beginning the 
experiment, the circuit is closed and the time ob- 
served. At the instant of closing circuit, the person 
closing it will say " Now ! " and at that instant the 
exact time (hour, minute, and second) is noted. The 
warning word " Ready ? " should be given a few sec- 
onds before the signal " Now ! " 

[If the dynamo current is used, the teacher or a student will 
close the circuit by means of the switch at the demonstration 
table, all other openings having been previously closed. If 
the batteries are used at the students' tables, one student closes 
the circuit at the commutator in each circuit and another ob- 
serves the time.] 

GO While the current is passing, a series of 
galvanometer readings is taken, tenths of the small- 
est scale divisions being estimated, and parallax 
carefully avoided. Read the angle of deflection at 
each end of the pointer. Reverse the current through 
the galvanometer by shifting the commutator as 



MAGNETISM AND ELECTRICITY 129 

nearly instantaneously as possible, and again read at 
both ends of the pointer. Before each reading, tap 
very gently on the frame, so as to overcome the 
slight friction at the pivot. Obtain as many sets of 
four readings each as the time of collecting the gas 
will permit, and record all the readings in a neat 
tabular form. 

(#) When the tube is nearly full of gas (hydrogen), 
the circuit is to be opened and the time recorded pre- 
cisely as at the beginning. 

(Ji) Raise or lower the tube in the vessel as may 
be necessary, until the liquids are at the same level 
inside and out. If the voltameter vessel is not deep 
enough, transfer the tube to a jar. 

Caution! Avoid heating the part of the tube 
containing the gas, either by breathing upon it or 
handling. Use a wooden holder or a thick band of 
paper. Now read and record the volume of gas 
above the acid surface in the tube. Read as before, 
from the bottom of the meniscus. 

(J) Note the temperature, and also the barometer 
and attached thermometer readings. 

Data. — Tabulate the results as indicated (p. 130). 

Remarks. — If the source of current be a dynamo or storage 
battery, all the instruments at the students' tables may be in 
series with it, and the current must be cut down to a safe and 
convenient strength by means of an adjustable resistance placed 
in the circuit and regulated by the teacher. An advantage of 
connecting all in series is that since all are measuring the same 
current, the teacher can measure it with a meter at the demon- 
stration table, and check the students' results by comparison 
with his own as well as with those of all the class. 



130 LABORATORY EXERCISES IN PHYSICS 
Numerical Data 



Time starting 


h. — m. — s. — 


Deflections 


Time stopping 


h. — m. — s. — 


1 


o 


Time interval T 


sec. 


2 




Tube reading (1) 


cc. 


3 




Tube reading (2) 




4 




Volume (2)-(l) V 




1 




Temperature (1) 


°C 


2 




Temperature (2) t 


°C 


3 




Barometer reading- 


inches 


4 




Attached thermometer 


°F 


1 




Temperature correction 


inches 


2 




Corrected barometer 
reading, B 


mm. 
inches 


3 




Vapor pressure p 


mm. 
inches 


4 




Net pressure P 


inches 


mean, a 


o 


Corrected volume V 


cc. 


tangent, 
a 




Current strength C 


amp. 


constant, 
K 





MAGXETISM AXD ELECTRICITY 131 

If battery cells are used at each table, the circuit should be 
opened at 22, and a box of resistance coils inserted. By means 
of this the current is to be regulated, so that the galvanometer 
needle may indicate constantly a deflection of nearly 45°. About 
four Daniell or gravity cells will be needed at each table. If it 
is not convenient for all to begin and close the experiment at the 
same instant, the current may be allowed to flow all the time; 
and the experiment is begun at each table by quickly placing 
the tube over the cathode, the time signal being given at the 
same instant. The tube should be previously inverted in the 
acid, but held aside from the electrodes, so that no stray gas 
bubbles can enter it. The experiment may be ended similarly 
by removing the tube from over the electrode to its first position. 

Calculations. — (a) The time interval is to be re- 
duced to seconds. The barometer reading is to be cor- 
rected for temperature as in Exercise 16. The vapor 
pressure depends on the strength of the acid and the 
temperature, and may be taken from a table (see 
Stewart and Gee. p. 497) and given to the class 
by the teacher. The net pressure is the corrected 
barometer reading minus the vapor pressure. 

( V) The volume is reduced to what it would be 
under standard conditions of temperature and press- 
ure by substituting the observed volume, net press- 
ure, and observed temperature for V. P, and t in the 
following formula for the laws of Boyle and Charles, 
and calculating the value of V , the corrected volume. 

v = VP x 273 

30(273 + 0* 
If P is given in millimeters instead of in inches, the 
corresponding pressure factor in the denominator 
should be 760 instead of 30. 



132 LABORATORY EXERCISES IN PHYSICS 

(<?) To calculate the current, (7, first find the num- 
ber of cubic centimeters of hydrogen given off in one 
second and then divide by the number of cubic cen- 
timeters liberated by one ampere in one second, thus : 

T x .1156 

(jp) Calculate the value of the constant, K, by the 

formula 

0= K tana. .*. K= > 

tan a 

in which a is the mean angle of deflection. 

Sources of Error. — (a) The temperature of the 
gas may not be the same as that indicated by the 
thermometer. 

(5) Time may be lost during the reversals of the 
current. A correction for this may be easily estimated 
and applied. 

(V) The most serious errors are those arising from 
the imperfections of the galvanometer. 

(d) Errors arising from the other observations 
have been considered in previous experiments. 

Note. — If the teacher so directs, the corrections of the ba- 
rometer reading for temperature and the corrections for vapor 
pressure are to be omitted. 

Lessons. — This experiment teaches an important 
quick method of current measurement and its use in 
standardizing a galvanometer. The constant, K, 
being known, if the galvanometer is a fairly good 
one, the current strength corresponding to any ob- 



MAGNETISM AXD ELECTRICITY 133 

served mean deflection may always be calculated by 
the formula C = iTtan a. 

Electrical energy is a commodity. It is a most important 
factor in our modern industrial development. Accurate meas- 
urements of electromotive force, resistance, current strength, 
inductance, capacity, etc., are all for the purpose of getting at 
the amount of energy consumed in the various machines and 
appliances by T^hich it is produced or utilized. Keep a lookout 
for such appliances, and try to find out how they make this 
energy available, and how the energy they produce or consume 
is measured. 



Exercise Number 25 
short distance telegraphy 

References 

A 432-434 GE 379, 380 JJ 290-298 

C 316 GP 550, 551 S 229 

C & C 507-510, 512, H 419-421, 424, 427 T 499, 500 

513 H & W 252 W & H 286 

Purpose. — The purpose of this exercise is to set 
up a short distance telegraph line of two stations, to 
diagram the arrangement, to trace the current 
through the circuit, to operate the instruments, and 
to explain their action. 

Apparatus. — (a) Call the two stations A and B. 
At each station there should be one gravity cell, one 
key, one sounder, some pieces of wire, and a couple of 
double connectors. 

(J) A single wire representing the line wire is 
supported on insulators and runs from A to B. 



134 LABORATORY EXERCISES IN PHYSICS 



ADJUSTING SCREWS-, 
CONTACT n 



BUTTON 




Operations. — (a) At one station, e.g. A, connect 
the — electrode of the battery cell to a wire leading 

from a gas pipe or 
water pipe. Both 
wire and pipe 
should have been 
filed till bright, and 
the wire tightly 
wound a half-dozen 
times round the 

Fig. 35. —Morse Key. 

pipe, or still better, 
soldered to the pipe, thus securing a good " ground 
connection." 

(6) At the other station make a similar ground 
connection with the + electrode of the battery 
cell. 

(<0 At each station, connect the free electrode of 
the battery with 
one terminal of 
the key. Here 
and throughout, 
use double con- 
nectors where 
there are no bind- 
ing-posts. 

(d) Draw a 
neat and legible 

diagram of the Fig. 36. -Telegraph Sounder. 

cell and connections as far as now made. 

00 At each station connect the free terminal oi 
the key with one of the binding-posts of the sounder. 



'ADJUSTING SCREWS- 




ELECTRO MAGNET 
SPRING 
BINDING POSTS 



MAGNETISM AXD ELECTRICITY 135 

(/) Join the other binding-post of the sounder 
to the line wire. The " circuit " is now complete or 
"closed'' and the apparatus is "in series." 

(^) Before attempting to operate, see that both 
keys are closed by means of their side levers, or 
"switches," which are provided in order that the 
keys may always be closed when no message is 
being sent. (Why?) Now complete the diagram of 
the circuit, including all the apparatus at both stations 
and the line wire, and having due regard to the pro- 
portions of the different parts of the apparatus. 

(K) By means of arrows, trace the path of the cur- 
rent from the zinc of your cell — through the fluid, 
then through the entire wire circuit, instruments, 
line, and ground — back to the zinc. 

(i) Xow operate the circuit, sending from each 
station in turn such Morse signals as may be indi- 
cated by the teacher. 

(j) Make a separate sketch or diagram of the key 
and of the sounder. By reference to the parts as 
indicated by appropriate lettering briefly explain the 
action of each. Draw from the objects, not the cats. 

Precautions. — Since oxidized, greasy, or loose 
connections greatly diminish the current strength 
(Why?), see that all connections are scraped bright 
and clean and that the binding screws are firmly set. 

Lesson. — This exercise is designed to make the 
student acquainted with the proper method of set- 
ting up the instruments of a telegraph line, and with 
the manner in which the electric current is used in 
sending and receiving signals with them. 



136 LABORATORY EXERCISES IN PHYSICS 



Exercise Number 26 



LONG 


DISTANCE TELEGRAPHY 
References 




A 432-434 


GE 379-381 


S229 


C316 


GP 550-552 


T 499-501 


C & C 511-514 


H 423-425 
JJ 290-299 


W & H 286 



ARMATURE CONTACT 
POINTS 



ELECTRO MAGNET 



Purpose. — The purpose of this experiment is to 
study the construction and action of the relay, and 
to learn why it is necessary on a line of high resist- 
ance. 

Apparatus. — (a) In addition to the apparatus of 
Exercise 25, a relay and two more cells of battery 

are needed at each 
station. 

(5) The same 
line wire may be 
used, but is sup- 
posed to be many 
miles longer, so 
that the additional 
resistance makes 
the current too 
weak to operate the sounder. If the teacher desire, 
he may insert a suitable resistance to represent that 
of the additional line wire. 

Operations. — (a) Examine the relay, and deter- 
mine which pair of binding-posts is connected with 
the ends of the magnet wire. These are called the 
main line posts. 




Fig. 37.— Telegraph Relay. 



MAGNETISM AND ELECTRICITY 137 

(J) The other two are called the local circuit posts. 
Trace the metallic paths from them to the air gap 
between the platinum contact point on the lever and 
that on the screw against which the lever strikes 
when the armature is attracted toward the magnet. 
Notice, when the armature is released and the lever 
flies back in obedience to the tension of its spring, 
that the screw against which it now strikes is in- 
sulated from it by a tip of hard rubber. Thus there 
is a break in the metallic path between the two local 
posts when the armature is not attracted; but this 
air gap is closed whenever the armature is drawn 
forward. 

(e) If a battery cell and a sounder be placed in 
series with the two local posts, can the relay lever be 
operated by the hand, so as to act as a key, and thus 
to work the sounder ? Why ? Try it, and state 
what occurs. 

(<f) Now (at each table) disconnect the local wires 
from their posts, join two cells in series, " ground " 
the —electrode of this "main line battery" at sta- 
tion J., and also ground the + electrode of the main 
line battery at station B. At each station connect 
the other — electrode of the main line battery to one 
post of the key ; connect the other post of the key 
with one of the main line posts of the relay ; and 
join the free main line post of the relay to the line 
wire. 

(e) Diagram the arrangement, and, by means of 
thin arrows, trace the main line current throughout 
the circuit. 



138 LABORATORY EXERCISES IN PHYSICS 

(/) Send a signal from each station to the other 
in turn. If you fail to receive the signal, first see 
that the circuit is unbroken excepting at the sending 
key, and then, if you still fail, ask the instructor to 
assist you in adjusting the relay. 

(#) Connect the local battery and sounder in series 
with the local posts of the relay, as you did in opera- 
tion (V). Can you now operate the relay at B by 
opening and closing the key at A (the key at B re- 
maining closed) ? Does the relay at A receive sig- 
nals sent from B in like manner ? Do the relays at 
A and B, when thus operated, open and close their 
respective local circuits so that the sounders click in 
unison with them ? 

(h) Add the local circuits to your diagram, tracing 
the local batter y currents through them. Use thick 
arrows to indicate that these currents are not the 
same as that on the main circuit, and are stronger. 

Lessons. — (a) Does the relay in operation (/) 
act just as the sounder did in Exercise 25 ? Does it 
make noise enough to be heard easily, or is the noise 
faint compared with that made by the sounder in 
Exercise 25 ? If the main line resistance be great, 
can the current work the sounder when connected as 
in Exercise 25 ? Why ? Is it, nevertheless, strong 
enough to operate the relay ? Does the relay lever 
act like a key to the local circuit ? How does it 
differ from a key with regard to the immediate source 
of the energy that moves it ? Does the sounder now 
make noise enough to be heard easily ? Is it the main 
battery current, or the sound, which is reenforced by 



MAGNETISM AND ELECTRICITY 139 

the use of the local battery and sounder ? State 
whether or not any of the local current gets into the 
main cfircuit, or any of the main line current into the 
local circuits. 

(5) From the object, make a careful drawing of the 
relay, and briefly explain its action. Do not repeat 
any statements made in answer to questions above. 

Exercise Number 27 
induced currents 

References 

A 388, 389 GP 515-521 S 232, 233 

C 229-305 H 396-398 T 222-226 

C & C 480-181 H & W 259-263 W & H 313-315, 

GE 356, 357 JJ 132-138, 110-112 327-329 

Purpose. — It is proposed in this exercise to in- 
vestigate the laws of induced currents. 

Apparatus. — The appliances consist of a coil of 
many turns of fine wire (secondary), and another of 
fewer turns of coarser wire (primary), which fits into 
the former ; a soft iron core, a bar magnet, a sensi- 
tive galvanometer (D'Arsonval or astatic), and two 
cells in series. 

Operations. — (a) Set up the galvanometer and 
connect its terminals by means of a shunt ; touch the 
galvanometer terminals to the leading wires from the 
battery, and make note of the direction of the current 
which gives a deflection to the right, so that in the 
experiments the directions of the induced currents 



140 LABORATORY EXEBCISES IN PHYSICS 

may be observed by noting the directions of the 
resulting deflection. Remove the shunt. 

(6) Connect the galvanometer terminals by long 
wires with the terminals of the secondary coil, keeping 
the coil and galvanometer as far apart as practicable. 

(<?) Thrust the north-seeking pole of the magnet 
into the secondary, note the deflection, and trace the 
direction of the induced current around the coil. 

(rf) From the direction of this current around the 
coil, determine the direction of its lines of force 
(Exercise 21), and state whether it caused the end 
of the coil into which it was thrust to be a north- 
seeking or south-seeking pole. 

Remember that if the current circulates counter-clockwise 
around the coil as you face its end, the lines of force come out 
of it ; and this end is a north-seeking pole. 

(e) Was the force of the coil in such a direction 
as to oppose or to assist the motion of pushing the 
north-seeking pole up to the coil ? 

(/) Now withdraw the north-seeking magnet pole, 
and note deflection, direction of current, direction of 
lines of force, and effect on the motion, as before. 

(</) Repeat all the observations and notes, using 
the south-seeking pole of the magnet. 

. Qt) Connect the terminals of the primary coil with 
the battery; determine one of its poles from the 
direction of the current around it, or by a compass 
needle (Exercises 20, 21); and then repeat all the 
experiments and notes made with one pole of the 
magnet. 

(i) Reverse the current through secondary. Does 



MAGNETISM AND ELECTRICITY 141 

its polarity change ? Repeat all the experiments and 
notes as with the other pole of the magnet. 

(j) Repeat all the experiments with the two coils, 
having previously placed the soft iron core inside the 
primary (J). State whether the quality or magnitude 
of the effects has changed, and how. 

(&) Place the primary inside the secondary, and 
then (1) close circuit ; (2) open circuit ; (3) reverse 
the battery wires and close circuit ; (4) open the 
circuit. Note all the results and compare them, 
quality and quantity, with those obtained by insert- 
ing and ivithdr awing the coil while the circuit remains 
constantly closed. 

(V) Insert the primary into the secondary and the 
soft iron core into the primary. Now repeat all the 
experiments made in (&) and compare results. 

Inferences. — State the effect produced (a) by in- 
creasing the number of lines of force passing in a given 
direction through a closed coil, (5) by diminishing 
the number of lines passing in the given direction 
through the closed coil (all the movements that were 
made either increased or diminished them). (Why ?) 

(e) State how the magnitude of the induced 
E.M.F. is affected by the rate of change of the 
number of lines, which was increased or diminished 
in the various cases either by changing more lines or 
by quickening the motion so as to change the same 
number in less time. 

(cZ) State Lenz's Law, and say whether or not all 
the observations show that this law is verified in 
your experiments. 



CHAPTER VI 

SOUND 

Exercise Number 28 

speed of sound 

References 



A 184 


GE 180 


J 18, 24, 25, 31 


C 191, 192 


GP157 


S180 


C & C 180, 181 


H 189-191 
H & W 338 


W & H 339 



Purpose. — The purpose of the experiment is to 
determine the speed of sound in open air. 

Apparatus. — The appliances required are : (a) a 
surveyor's tape, or a bicycle with an accurate cyclom- 
eter attached ; (5) a stop-watch ; (<?) a pistol and 
some blank cartridges ; (J) two thermometers. 

Place. — This must be such as to furnish a straight- 
away stretch of open ground, level, and uninter- 
rupted by trees or buildings. A country road or 
railroad is best. Such a place can usually be reached 
by a car line or bicycles, even by classes in a large 
city. 

Operations. — (a) Measure off as long a distance 
as is available, — call the two stations A and B. 
They must be half a mile or more apart. If there 
are several bicycles with cyclometers, let all measure 

142 



SOUND 143 

the distance, average the results, and reduce to feet 
by multiplying by 5280. If the school own a sur- 
veyor's tape, let the distance be measured by that 
also, and the result averaged with that obtained by 
the cyclometers. 

(5) Let half the party go to station i?, and the 
rest remain at A. Let a person at A set the stop- 
watch, and be ready to start it when he sees the puff 
of smoke from the pistol. When he is ready he 
shows a white handkerchief to the person who is to 
fire the pistol at B. 

(e) Just before firing, B shows a handkerchief to A. 

(c?) The watch is started at the instant of seeing 
the puff of smoke, and stopped at the instant of hear- 
ing the sound. 

(e) Let different pairs of students repeat the 
operations, the teacher standing near the observer 
and judging each time whether the result of the trial 
is worthy to be recorded. 

(/) Now let the two parties exchange the pistol 
and watch ; and let them make a new set of obser- 
vations equal in number to the first set. The tem- 
perature should be taken several times at each station, 
the thermometer being screened from sun and 
wind. 

Data. — Record in tabular form, the values of the 
distance, ?, and of the time interval, £, observed by 
the first party, and of the time interval, #, observed 
by the second party, and of the temperature, T. 
Also record the average values of Z, £, £', and T. Add 
t and t ! and divide by 2 to get the mean time interval. 



144 LABORATORY EXERCISES IN PHYSICS 

Calculation. — Since speed = ——. , divide the 

time 

mean value of I in feet by the mean time interval in 

seconds. 

Sources of Error. — Since the time interval is very- 
small, and since the percentage error of the result 
cannot be less than that involved in measuring the 
time, the errors in the measurement of I will, there- 
fore, be relatively unimportant. 

The personal equation of the observers will be the 
most serious kind of error, and will be apparent in the 
variation of the individual values of t and t r from 
their averages. Unless the day is perfectly calm, 
the wind will increase the speed of the sound if 
travelling with it, and diminish the speed of the 
sound if travelling against it. 

This effect will be at least partially eliminated by 
observing at A and at B alternately. On account of 
the shortness of the time, the instrumental errors of 
the watch may also be serious. If the watch can be 
rated by reference to an accurate clock, the necessary 
corrections may be applied. 

Temperature Correction. — Reduce the observed 
value of the speed of sound to what it would be at 
0° C. by subtracting two feet per second for each 
degree that the observed temperature is above zero 
(S =S t -2t). 

Lesson. — This exercise illustrates the early 
methods of determining the speed of sound. In 
later methods the time of starting and arriving have 
been automatically recorded by means of the electric 



SOUND 



145 



current upon a sheet of paper moved by clockwork 
(chronograph). Thus the personal equation is 
nearly eliminated. 

Exercise Number 29 



VIBRATION FREQUENCY OF A TUNING-FORK 



A 192-198, 201 
C 199, 212, 213 
C & C 204-208, 226 
GE 174, 192-194 



References 

GP 173-176 
H 186, 206-212 
H & W 335, 344 

J 7, 9, 39 



S 181, 183 
W&H 344 



Purpose. — The purpose of this exercise is to rate 
a tuning-fork, or, in other words, to determine the 
number of vibrations which it makes in one second. 

Apparatus. — A pendulum and a fork are mounted 
on supports fixed to a long board, so that, when they 
are vibrated simultaneously, the styluses that are 
attached to them will trace lines very near together 




Fig. 38. — Apparatus for rating a tuning-fork. 



146 LABORATORY EXERCISES IN PHYSICS 

along a strip of smoked glass. When the glass is 
drawn swiftly along the board each stylus traces a 
wavy line, and the line traced by the pendulum 
crosses and recrosses the line traced by the fork. 
The height of the fork above the glass, and also that 
of the pendulum, is adjustable by means of a clamp 
or screw so that the point of each stylus can press 
very lightly against the glass. A piano-hammer or 
a little mallet of soft wood is used to set the fork 
and pendulum to vibrating. 

Operations. — (a) Rate the pendulum as described 
in Exercise 11, Part A. Record three ratings, and 
take their average as the number of vibrations made 
in one second by the pendulum. 

(J) On a block of wood ignite a lump of camphor 
about the size of a pea, and, holding the glass hori- 
zontally about a half-inch above the burning cam- 
phor, move it slowly backward and forward until its 
under surface is entirely covered with a thin layer of 
soot. 

(c) Now lay the glass on the board, blackened 
side up. The styluses should be lifted when doing 
this, so that they will not be bent out of their 
positions. The styluses should now press very 
lightly against the smoked glass near its end. See 
that the glass rests in such a position that it may be 
quickly pulled along the board in the direction of its 
length, so as to allow the fork and pendulum to trace 
their vibrations on it while it is moving. The speed 
with which the plate ought to be moved must be 
•learned by practice, and is twice as great for a fork 



SOUND 147 

making 256 vibrations as for one making 128 vibra- 
tions. (Why ?) 

(cT) Set the fork and pendulum to vibrating, and 
slide the plate. 

If the trial is successful, a set of tracings like 
Fig. 38 a will be obtained. It is well to get at least 
two good traces on the plate. 

Each of the spaces, ac, bd, ce, df, etc., represents 
the time occupied by one vibration of the pendulum. 
(Why ?) Also each space from crest to crest or from 




Fig. 38 a. — Showing the appearance of the smoked glass after taking 
the tracings. 



trough to trough of the wavy line traced by the fork 
represents one complete vibration of the fork. Count 
the number of vibrations and tenths of a vibration of 
the fork traced between a and <?, c and e, e and g, 
and so on. Make and record at least three different 
counts. The average of these counts is the number 
of vibrations made by the fork while the pendulum 
makes one vibration. 

Data. — Tabulate the numerical data. 

Let n be the number of complete vibrations which 
the fork makes while the pendulum is making one 
complete vibration ; let iV^ be the number of complete 
vibrations made by the pendulum in one second, and 



148 LABORATORY EXERCISES IN PHYSICS 

let N f be the number of complete vibrations made by 
the fork in one second. 

Then N f = N p xn. (Why ?) 

A ranch more accurate method of treating the observations 
is to connt the whole number of vibrations and the fraction of 
a vibration that were made by the fork while the pendulum made 
three or more vibrations. Divide the former number by the 
latter to get the n of the above formula. In making the count 
it is well to mark on the glass every tenth vibration of the fork. 
The difficulty in applying the method suggested above lies in 
the fact that it is hard to get a good trace of the required 
length with the apparatus usually supplied. 

Sources of Error. — (a) Since the two styluses are 
necessarily a little distance apart, errors will arise from 
changes in the speed of the plate during its motion. 

(5) Errors are involved in estimating the fractions 
of a vibration. 

(<?) What errors are involved in rating the pen- 
dulum ? 

Lessons. — (a) From a table of the notes of the 
standard scale and their corresponding vibration 
numbers, choose that note to which the vibration 
number of the fork that you rated most nearly 
agrees; and call this the note given by the fork. 

(6) See if the fork is in tune with the corre- 
sponding fork of a standard set by sounding them 
together and listening for " beats." 

(e) Compare the notes given by this fork and 
another of different frequency which has been rated 
by another student, and state what effect the vibra- 
tion frequency of a sounding body has on the note 
given out by it. 



SOUND 



149 



Exercise Number 30 



WAVE LENGTH OP A TONE 



A 205 
C 173, 174 
C & C 191-194 



References 

GE 187-189 
GP 168-170 
H 198-202 



J 56, 58, 61, 62 

S 184 

W & H 352 



i 



p 



Purpose. — It is proposed to determine the wave 
length of the tone given out by a tuning-fork. 

The method consists in measur- 
ing the length of the air column 
that will give resonance to the fork 
and in deducing therefrom the 
length of the waves. 

Apparatus. — (a) The tuning-fork 

should be one making not less than 

256 vibrations, and preferably the 

one whose vibration number has 

been determined in the preceding 

exercise. 

^ — : — : — v 

(5) A glass tube not 
less than eighteen inches 
long, and having an inside 
diameter of not less than 
an inch, is mounted on a 
suitable support and pro- 
vided with a convenient 
means of varying the 
length of the column of 
Fig. 39. a ir contained in it. 




Fig. 39 a. 



150 LABORATORY EXERCISES IN PHYSICS 

Two very convenient forms of apparatus are shown 
in Figs. 39 and 39 a. Water is used as a piston, its 
level in the tube being easily and accurately adjusted 
in the manner suggested by the illustrations. 

Operations. — (a) Set the fork in vibration Jby 
striking it with a piano-hammer, or a little mallet 
made of soft wood, and place it close to the mouth of 
the tube in such a position that one of the prongs exe- 
cutes its vibrations in the line of the axis of the tube. 

(5) Make the air column evidently too short, and 
increase its length until a strong resonance occurs. 

(e) By repeated trials test the adjustment, and 
try to fix it between definite limits. 

(c?) When satisfied that the length of air column 
corresponding to maximum resonance has been fixed 
within the smallest limit, record the amount of this 
limit, and, with a rule, measure and record the length 
of the air column, i.e. the distance from the water 
to the end of the tube/Repeat the operations as 
many times as the time will permit, and record all 
the observations in tabular form. 

Calculations. — Take the average of the numbers 
representing the length of the resonant air column. 
Theoretically, this is \ the length of the wave, but 
experiments have shown that the diameter of the 
tube affects the length of the resonant column. A 
correction equal to \ the internal diameter of the 
tube should be added to the mean length of the 
latter as determined above. 

The wave length of the tone given out by the fork 
is then obtained by multiplying the corrected length 
by 4. (Why?) 



SOUND 151 

Resonance occurs when the air column is f or J the wave 
length, but these cases are not here considered. 

Sources of Error. — The most important error is 
that involved in the judgment of the observer as to 
when the loudest resonance occurs. State the dis- 
tance through which the piston had to be moved each 
way from the position for maximum resonance before 
the sound became unmistakably fainter. What per 
cent is it of the length of the column ? The percen- 
tage error of the result cannot be less than this unless 
the mean of a long series of observations is taken. 

Lessons. — (a) This exercise is intended to famil- 
iarize the student with the theory of resonance, and 
afford practice in a simple method of directly deter- 
mining wave length. 

(5) Since a wave traverses a distance equal to its 
own length during one complete vibration, it is clear 
that the velocity of sound or the distance traversed 
in one second = wave length x vibration frequency. 
Calculate the velocity of sound from the wave length 
and the vibration frequency of the fork. Compare it 
with the velocity obtained in Exercise 28. In order 
to compare them, the units of length must, of course, 
be the same, and both values must be reduced to 
what they would be at 0° C, as in Exercise 28. 

Knowledge of wave lengths and of the various methods of 
measuring them is of little direct practical value, but has proved 
to be immensely important in developing the theory of air waves 
and ether waves. In consequence of this theoretical knowledge 
musical instruments have reached increased perfection ; and the 
discovery of wireless telegraphy became possible. 



152 LABORATORY EXERCISES IN PHYSICS 

Exercise Number 31 

cause of overtones 

References 

A 199, 200 H 221, 223-225 

C 200, 209 H & W 336 

C & C 210, 211, 213-215, 220-222 J 54-55 

GE 195, 197 S 182 

GP 179-182, 185, 186 W & H 348, 356-359 

Purpose. — The purpose of this exercise is to de- 
termine the positions of the nodes and segments of a 
musical string when vibrating under certain condi- 
tions, and to investigate the relations of these nodes 
and internodes to the overtones given out by the 
string. 

Apparatus. — A sonometer, which consists of two 
piano wires stretched over a pair of frets at the ends 
of a suitable sounding-board. The wires pass over a 
fixed bridge near one end and differing tensions may- 
be applied to them by means of weights or spring 
balances. A movable bridge is also provided. If the 
tensions are applied by means of weights, pulleys, 
or levers shaped like the quadrant of a circle, are used 
to change the direction of the forces from horizontal 
to vertical. 

A violin bow, a cake of rosin, and a number of 
bent paper strips, to be used as riders, are also 
required. 

If no sonometers are available, the wires may 
be stretched over the laboratory table ; and wooden 



SOUND 



153 



wedges placed thereon take the place 
of the bridges. If spring balances are 
used, they may be so arranged that 
the tensions can be accurately adjusted 
by means of a pair of long screws 
which pull in the lines of the wires. 



Part A 

Operations and Observations. — (a) 

See that the sonometer is securely 
fastened to the table by means of a 
clamp or handscrew, and that the ten- 
sions draw the wires in horizontal 
lines parallel with the length of the 
sounding-board. The wires should 
rest but lightly on the frets that are 
next the stretching forces. 

(5) Insert a movable bridge so that 
the length of one of the wires between 
the two bridges shall be (say) one meter. 
Now bow the wire near (not at) the 
middle. Can you see the part between 
the bridges vibrating as a whole ? 
Apply such a tension as will cause the 
wire to give a full round note. Drop 
paper riders so that they will bestride 
the wire at several points along its 
length. What happens to the riders? 
What does this indicate about the 
condition of the wire at the places 
where the riders were placed ? 



6 



154 LABORATORY EXERCISES IN PHYSICS 

By repeated trials ascertain whether there is any 
part of the wire that is not in vibration when it has 
been bowed or plucked near its middle point. 

(c) Carefully listen to the tone and try to keep it 
in mind. It is called the fundamental tone of this 
string, with the given length and tension. State 
whether the string vibrates as a whole when it gives 
its fundamental tone. Where are the nodes, or sta- 
tionary points? Illustrate the condition of the string 
and the behavior of the riders by a diagram. Write 
" Fundamental " beneath the diagram. 

(c?) Place riders at the ends and at the three 
points which divide the string into fourths. Call 
the riders and the points at which they are placed 
0, ^, |> f, and 1. Now press, not too heavily, with 
the finger upon ^ and apply the bow near 0. Imme- 
diately after the bow is removed, remove the finger 
also. Which riders remain quiet and which are 
agitated? Repeat until sure that certain riders 
remain quiet while certain others are violently dis- 
turbed. State the conditions of the points of the 
string where the riders had been placed. Illustrate 
by a diagram as in (e). Mark the nodes on the 
diagram. The vibrating parts between the nodes 
are called internodes or segments. Mark them also 
on the diagram. 

(e) Repeat the operation once more and listen to 
the note given out by it. Compare it carefully with 
the fundamental by sounding first one and then the 
other. (To sound the fundamental, you have only 
to remove the finger from the point J.) Is it the 



SOUND 155 

octave of the fundamental ? If so, make another dia- 
gram and write " Octave " beneath it. 

(/) Place riders at points 0, 1, 1, 1 f, |, and 1. 
Repeat the former operations, but damping with the 
finger at ^ and applying the bow at point near 0. 
Make sure of the positions of the nodes and segments 
before trying the next case. Illustrate by diagram 
as before, marking nodes and segments. 

(g) Listen to the tone given out by the string 
when vibrating as it does in this case and compare 
it with the fundamental and the octave. Is it the 
fifth (or sol) above the octave ? If so, write "Fifth 
above the Octave" under the diagram. 

Qi) Place riders at points dividing the string into 
eighths and make experiments similar to the preced- 
ing. Damp at \ and bow near 0. 

Illustrate by diagram as before, marking nodes and 
segments. 

(i) Compare the resulting tone with the funda- 
mental and first octave. Is it the second octave? 
If so, write "Second Octave" beneath the diagram. 

Part B 

(a) Bow the string (without damping) near the 
point 0, and listen carefully to the note. Can you 
detect the octave, the fifth above the octave, or the 
second octave sounding along with the fundamental ? 
If you are sure that you can detect any of these, 
record the fact. 

(J) Bow near and afterward damp the wire by 
touching it very lightly with a feather or a bit of blot- 



156 LABORATORY EXERCISES IN PHYSICS 



ting-paper at \. Does the fundamental cease ? Do 
you hear the octave ? If so, record the fact. Can 
you infer from this that the octave and the funda- 
mental were sounding at the same time before the 
wire was damped at ^ ? Was the wire vibrating as 
a whole and in halves at the same time ? Why did 
the octave come out more clearly after damping ? 

(<?) Bow near and damp with the feather at ^. 
Does the fundamental cease ? Do you hear the fifth 
above the octave ? Can you make inferences similar 
to those of (K) ? State them. 

(d) Bow near and damp at \. Make a set of 
observations and inferences similar to those made in 
(5) and (V), but applying to the second octave and 
four vibrating parts. 

Data. — Copy the tabular form and fill the blanks. 



Point where bowed 


i 

2 





9 


9 


Point where damped 


— 


i 

2 


9 


9 


Number of nodes 


2 


3 


? 


9 


Number of segments 


1 


9 


9 


9 


Resulting tone 


Funda- 
mental 


Octave 


9 


9 



Inferences. — (a) State whether from your experi- 
ments you are justified in inferring that a string or 
wire can vibrate as a whole and in parts at the same 
time. 



SOUND 157 

(5) State the number of vibrating parts or seg- 
ments which correspond to fundamental, the octave, 
the fifth above the octave, and the second octave, 
respectively. 

(e) Define an overtone. 

(c?) When the tones mentioned in (5) are present 
as overtones, what is the cause of their presence along 
with the fundamental ? 

(e) State whether or not you can discern any 
difference in the quality of the tone, first when the 
overtones accompany the fundamental, and then when 
they do not accompany it. 

• 

Exercise Number 32 

laws op vibrating strings — length 

References 



A 209, 210 


C & C 210-212 


H 220-222 


S186 


C215 


GE196 


H & W 339 


W & H 347 




GP179 


J 50-53 





Purpose. — The purpose of the experiment is to 
verify the law for the relation of the length of a 
stretched string to its vibration number. 

Apparatus. — This is the same as that used in the 
preceding exercise. A second movable bridge is 
necessary. 

Operations. — (a) Adjust the movable bridge so 
that the vibrating part of one wire, J., is (say) one 
meter long, and increase the tension until the wire, 
when bowed or plucked near the fixed bridge, gives 



158 LABORATORY EXERCISES IN PHYSICS 

a good clear note. Call this note do v and adjust the 
tension and length of the other wire, 2?, so that it 
gives the same note. It is to be used for reference. 
Students who have studied music will tune the two 
strings to unison without difficulty. Those who have 
not trained musical ears can tune the second string 
until they begin to hear beats, and then cautiously 
shift the bridge or change the tension until the beats 
can no longer be heard. While the two strings are 
sounding together, as unison is approached, the beats 
diminish in number. 

(£) Move the bridge under A to such a point as to 
make the length of the vibrating part exactly -| what 
it was at first, and sound A and B successively. 

If necessary, hold the wire against the movable 
bridge by pressing lightly against it with the finger 
at a point just outside the bridge. 

Repeat several times. Do you recognize the inter- 
val known in music as do^mi^ (major third) ? If 
so, record it. If the two strings do not seem to give 
this interval accurately, restore the bridge to its 
original position, and test the two strings to see if 
they are in tune, then repeat the operation. 

(e) By means of the movable bridge reduce the 
length of the vibrating part of A to -| of its original 
length, and repeat the previous operations. Is the 
interval do x -sol x (major fifth) ? Test as before. 

Leaving A of the length to sound sol v carefully 
tune B to unison with it (by means of its movable 
bridge). Now make the length of the vibrating part 
of A exactly \ what it was at first, and observe the 



SOUND 



159 



musical interval as before.* Is it sol 1 -do 2 ? If neces- 
sary, make sure by testing the two wires for unison 
when sounding sol v and repeating the observation. 

(d) If time permits, tune B to unison with A at 
do v and then reduce the length of A to J. Observe 
and test the interval as in the previous operations to 
learn if the interval is do 2 -sol 2 . 

Data. — Tabulate results as follows, appropriately 
filling the blanks : — 



Length 


100 an. 


so 


66.66 


50 


33.33 


Length ratio : 
New length 
Original length 


. 1 


4 
5 


2 
3 


l 

2 


l 

3 


Xew note 


clo l 


9 


? 


? 


? 


Interval 


Unison 


? 


? 


? 


Octave 
+ fifth 


Vibration ratio of 
interval: new 
note to funda- 
mental 


1 


4" 


9 


? 


? 



Sources of Error. — Errors may arise from unob- 
served changes of adjustment, but the most serious 
error, of course, lies in the judgment of the hearer as 
to the accuracy of the interval. This experiment 
may be performed with much greater accuracy and 
completeness by using one string and a set of stand- 
ard forks of known vibration numbers, and tuning 
the string to unison with each fork in turn by chang- 



160 LABORATORY EXERCISES IN PHYSICS 

ing the length only. The lengths and vibration 
numbers can then be directly compared. This 
method, however, is not adapted to the equipment of 
most elementary laboratories. 

Inferences. — Compare the ratio between each new 
length and the first length with the ratio between 
the vibration number of the corresponding new note 
and the fundamental. What must be done with each 
ratio of the vibration numbers in order to make it 
equal to the ratio of the corresponding lengths ? 
State the relation of the frequencies of the notes to 
the corresponding lengths of the string. This is 
sometimes called the First Law of Vibrating Strings. 

Exercise Number 33 
laws of vibrating strings — tension 
Eeferences. — These are the same as those for Exercise 32. 

Purpose. — The law that states the relation of 
tension of a string to the vibration number is to be 
verified. 

Apparatus. — The apparatus used in Exercises 31 
and 32 is to be used in this experiment. 

Operations. — (a) The two wires are put under 
tensions of about two or three pounds each. The 
tensions should be made as nearly as possible exactly 
equal. The movable bridge is then adjusted under 
both wires at such a distance from the fixed bridge 
that the vibrating parts of the two wires are of equal 
length. If the tensions and lengths are exactly equal, 



SOUND 161 

and the diameters and materials of the two wires the 
same (as they should be), the two wires when sounded 
together will be in unison. 

If beats are noticed, go carefully over the adjust- 
ments of length and tension until these adjustments 
are correct and the two wires are in tune. 

(5) Increase the tension of the wire A until it is 
four times as great as before. If using the spring 
balances, do not forget to allow for the zero correc- 
tion as in Exercises 5 and 6. Is the resulting note 
the octave of the first ? Sound B and A successively 
and compare the notes. By means of a movable 
bridge make B half its original length, so that it 
will give the octave of the first note. Are the two 
strings again in unison ? If not, go over the adjust- 
ments of tension of A and length of B, see that they 
are correct, and try again. If the two strings are not 
in exact unison, is the difference too large to be 
ascribed to such errors as are likely to exist in the 
adjustments of tension ? 

(c) Restore the two wires to their first condition 
and repeat all the operations, using a tension on A 
which is nine times as great as the first. Is the note 
sounded the fifth above the octave ? Make B one- 
third its original length, and test carefully as before 
to see if the two strings are in unison. 

Data. — Call the fundamental do v the octave do v 
and the fifth above the octave sol 2 . Tabulate the 
data. If the number of vibrations per second when 
do 1 is sounded is n, then that corresponding to do 2 
is 2 n. What is that corresponding to sol 2 ? 



162 LABORATORY EXERCISES IN PHYSICS 

Inference. — (a) Compare the tensions and the 
corresponding vibration numbers. What has to be 
done with the former in order to make the latter 
proportional to them ? 

(J) State the law that is verified by the observa- 
tions made in this exercise. 

Exercise Number 34 

laws of vibrating strings — diameter 

References. — These are the same as those for the two 
preceding exercises. 

Purpose. — The law of the relation of vibration 
number to diameter is to be verified. 

Apparatus. — This is the same as in the three pre- 
ceding exercises, except that the two wires used 
should have diameters which bear a simple relation 
to each other. If Nos. 22 and 28 B. & S. gauge are 
used (or 16 and 24), the diameters will be very nearly 
as two to one. A vernier caliper or micrometer 
caliper is needed for determining these diameters. 

Operations. — (a) By means of the movable bridge 
and a suitable tension, adjust the larger wire, A, so 
that it gives a clear note. Make the length and ten- 
sion of the smaller wire, B, exactly the same, and care- 
fully compare the two notes. Is the note given by 
B the octave of that given by A ? If not, go over 
the adjustments carefully. 

(J) Make A one-half the original length, and see 
if the two notes are in unison. Test the adjustment 
as in the previous experiments. 



SOUND 



163 



(c) Measure the diameters of the two wires. 
Data. — Tabulate under the following heads : — 



Diameter 



B 



Note 



do l 



Frequency 



Ratio Frequency A = ? 
Frequency B 



Ratio 



Diameter A 
Diameter B 



Sources of Error. — Briefly state the principal 
sources of error. 

Inferences. — (a) What must be done with the ra- 
tio of the frequencies in order to make a proportion 
with the ratio of the diameters ? 

(5) Can the lack of exact proportionality be fairly 
ascribed to experimental errors ? 

(?) State the law verified'in the observations. 

(d) Other things being equal, what is the relation 
of diameter to mass per unit length ? 

[Mass j = volume A x density = l 77 x (diameter 4 ) 2 

x 1 x density, and massj = volume^ x densitv = 4- ir 



mass , 



X (diameter^) 2 x 1 x density. 

What, then, is the relation of the vibration numbers 
of two strings to their masses per unit length? 

Try to find and understand applications of the laws of 
vibrating strings in various musical instruments. 



CHAPTER VII 

LIGHT 

Exercise Number 35 

bunsen's photometer. law op inverse squares 

References 



A 267, 268 


GP 286-288 


J 7-10 


C & C 238 


H 447-449 


S194 


GE 223-225 


H & W 276 


W & H 366, 367 



Purpose. — The purpose of this experiment is to 
verify the law of inverse squares for light by the 
method of Bunsen's photometer. 

Apparatus. — The photometer consists of a meter 
rule and three square blocks, each of the same thick- 
ness as that of the rule. The blocks can slide along 




A "^B C 

Fig. 41. — Simple form of Bunsen's Photometer. 

the table beside the rule, whose face is just flush with 
their upper surfaces. Each block has a pair of 
diameters accurately scratched upon its upper surface 

164 



LIGHT 165 

by means of a knife and square. One of the blocks. 
B. carries a pair of uprights, to which a screen of 
white paper may be attached by bits of soft wax. the 
centre of the screen being over the centre of the 
block. At the centre of this screen is a circular 
grease-spot (made by driving into it. with a hot 
flatiron. a bit of paraffin). One block. A. carries a 
single candle at its centre, and the third. C. a row of 
four candles set close together, two on each side of 
the centre of the block. The centres of the candles 
are on the diameter of the block, that is. perpen- 
dicular to the length of the rule. Shallow holes are 
bored into the blocks to receive the candles. The 
apparatus should be used in a thoroughly darkened 
room, and screened from the light of the other tables. 
or, better still, enclosed in a long box with chimneys 
at the ends, and with doors or opaque cloth curtains 
on the side toward the observer. With this latter 
arrangement the room need not be absolutely dark. 

Operations. — (a) See that the rive candles are all 
of the same height, and that their wicks are trimmed 
and bent down slightly, so that they give flames as 
nearly as possible of the same size. Trim them if 
necessary. 

(5) Place the blocks A and C against the rule near 
its opposite ends. 

(?) Slide the block B along the rule until the 
grease-spot ceases to be visible when seen from a 
point a little to the right of the edge of the screen, 
and read on the rule the position of the knife scratch 
upon which the screen rests. 



166 LABORATORY EXERCISES IN PHYSICS 

(cT) Now make a second setting in precisely the 
same manner, observing the spot from a position as 
far to the left of the edge of the screen as the first 
point of observation was to the right of it. Read on 
the rule the position of the knife scratch correspond- 
ing to the disappearance of the spot. Record the 
average of these two settings as the mean position of 
the screen. 

(e) Read the positions of the knife scratches on 
the blocks A and (7, and record them as the positions 
of the two lights. By subtraction determine the 
distances of the two lights from the screen. 

(/) Change the position of one of the lights, and 
repeat the settings. Make as many pairs of readings 
as the time permits. 

Data. — Record the results of each setting in a 
column, each result opposite its proper heading. 

Numerical Data 



Trials 






Readings, scratch A 






Readings, scratch B 






Readings, scratch C right 






Readings, scratch C left 






Readings, scratch C mean 







LIGHT 



167 



Numerical Data — Continued 



Distance A B 






Distance CB 






Ratio — 
AB 






Light emitted by A 


1 




Light emitted by B 


4 





Sources of Error. — State the errors which may be 
due to (a) the candles ; (5) the position of the ob- 
server, and his judgment ; (<?) light received by the 
screen from sources other than the direct rays of 
the candles. If all extraneous light be not excluded, 
the results will be thoroughly unreliable. 

Inferences. — We assume that when the spot dis- 
appears at the mean position of the screen, the two 
surfaces are illuminated with equal intensities. 

(a) If four candles, at distance CB, give the same 
illumination to the screen as one candle does at dis- 
tance AB, what is the intensity of illumination by 
one candle at CB as compared with that by one 
candle at AB ? 

(J) What must be done with the ratio of the 

CB 

distances — - - in order to make it equal to the ratio 
AB 

of the intensities with which one candle illuminates 
the screen at these two distances respectively. (Both 
ratios should be reduced by performing the indicated 



168 LABOBATOBT EXERCISES IN PHYSICS 

CB 

division.) If there is a decimal remainder to——, can 

AB 

it fairly be ascribed to experimental error? State 
the law that is verified in this case. 

Additional Work. — If the time assigned admits of further 
work, the four candles may be replaced in turn by three, two, 
and one, and the settings repeated. In this case, although it 
will not be so obvious, the ratio of the squares of the distances 
will be equal to the ratio of the number of candles used, 
as before. 



Exercise Number 36 
Alternative Method 

RUMFORD'S PHOTOMETER. LAW OP INVERSE 
SQUARES 

References 



A 267, 268 


GP 286-288 


J 7-9 


C & C 235-237 


H 441-449 


S194 


GE 223-225 


H&W276 


W & H 366 



Purpose. — In this exercise, the principle of Rum- 
ford's photometer is to be used to verify the law of 
inverse squares. 

Apparatus. — A white cardboard screen is tacked 
to a block so as to make the card stand upright. 
Two square blocks, A and i?, have their diameters 
marked or scratched on their upper surfaces, and are 
to be used as carriers for five equal pieces of candle. 
With chalk or pencil a perpendicular is drawn to the 
screen at its middle point. On this perpendicular, 



LIGHT 



169 



at about 5 cm. from the screen, is mounted a small 
cylindrical rod. (A penholder or a lead pencil stuck 
into a flat cork will do.) Through the axis of the 
rod are drawn two straight lines, pq and rs, making 




Fig. 42.— Rumford's Photometer. 

equal small angles with the perpendicular and meet- 
ing the screen. On the perpendicular is placed a 
second cardboard screen, so as to shield the two lights 
one from the other. 

Operations. — (a) At the centre of the block A 
mount one of the candles, and along the diameter of 
B mount the other four candles close together, and 
one behind another. 

(5) Light the candles, bend the wicks down a little, 
and let them burn for a few moments till their flames 
are of equal size. If necessary, trim them to make 
them so. 

(c) Move A along with a diameter on the line pq 
until the axis of the candle is, say, 25 cm. from the 
screen. Move the diameter of B along the line rs, 
and note the two shadows of the rod which are caused 



170 LABORATORY EXERCISES IN PHYSICS 

by the two lights. If the black parts (umbras) of 
these shadows are not close together, move the screen 
toward the rod until they are. 

(c?) Now, with the greatest possible care, slide B 
backward or forward along rs, as may be necessary, 
until it is in such a position that the two shadows 
appear equally dark. 

(e) Test the sensitiveness of the adjustment by 
moving the block forward or backward until each 
shadow in turn is manifestly less dense than the 
other. Record the amount of the change in distance. 
This represents your personal equation, or the dis- 
tance within which you can set with certainty. 

(/) Measure and record the distance from the 
screen to the middle of the line of four candles. Do 
this by measuring to the end of the block and adding 
half its diameter. 

(#) Place the candles so that the line joining their 
centres is perpendicular to rs and is bisected by it. 
Repeat (6?), (e), and (/). 

(A) Change the one candle to a distance of, say, 
40 cm. from the screen, and repeat all the previous 
operations. 

Data. — Record the quantities opposite their proper 
headings. Make a vertical column for each setting. 

Sources of Error. — State how errors may arise (a) 
in setting, (V) in reading distances, (e) in assuming 
that the candles radiate equal amounts of light. 

Inferences. — We assume that when the shadows 
are equally black the screen is equally illuminated 
by the two lights. 



LIGHT 



171 



Numerical Data 



Settings 


1 


2 


Distance pA 






Distance rB 






Ratio — 
pA 






Light emitted by A 


1 




Light emitted by B 


4 





(a) If four candles at the distance rB give the 
same illumination to the screen as one at distance pA, 
what is the intensity of the illumination by one can- 
dle at rB as compared with that by the one candle 
at pA? 

(5) What must be done with the ratio of the dis- 

rB 

tances — - in order to make it equal to the ratio of 
pA 

the intensities with ivhich one candle illuminates the 
screen, at these two distances respectively ? (Reduce 
both ratios to their lowest terms, expressing that of 
the distances as a mixed decimal number, if neces- 
sary.) 

(e) Can the decimal remainder be fairly ascribed 
to experimental errors ? 

(cty If so, state the law that has been verified by 
your results. 



172 LABORATORY EXERCISES IN PHYSICS 

Remarks. — This exercise can easily be performed 
at home in the evening, the distances being measured 
in inches by a foot rule or tape measure. If made in 
the laboratory, the room must be darkened and the 
apparatus surrounded by screens to cut off the light 
from the other tables. The Rumford photometer may 
be used to determine the candle power of a lamp, the 
calculation being similar to that of Exercise 37. 

Try to find applications of the Law of Inverse 
Squares in the best methods of distributing artificial 
lights in houses and streets, and in the use of lenses 
and reflectors for lighthouses and searchlights. 
Where does the law appear in Mechanics, in Electro- 
statics, in Magnetism, and in Sound ? 

Exercise Number 37 
photometry. candle power op a lamp 

References. — These are the same as those for Exercise 35. 

Purpose. — It is proposed to apply the law of in- 
verse squares in measuring the candle power of a 
lamp by the method of Bunsen's photometer. 

Apparatus. — In addition to the Bunsen's photom- 
eter, a kerosene lamp, gas burner, or incandescent 
electric lamp is supplied, also a small block or adjust- 
able support for the candle, by means of which it 
may be raised so that the centre of its flame shall be 
at the same level as that of the lamp. 

Operations and Data. — (a) Support the candle 
exactly over the centre of block A and the lamp over 



LIGHT 173 

that of B. Trim the candle wick, and elevate the 

candle till its flame is level with that of the lamp. 

(6) Make several pairs of settings exactly as in 

Exercise 35, tabulating the readings and distances as 

(OBY 
before. Record also the ratios ; - _/ . Perform the 

(ABy 

division for the result of each trial and tabulate the 
results. Record the average of these results as 
the candle power of the lamp. By reference to the 
law of inverse squares and the previous exercise, 

(OB") 2 
explain why the ratio p J represents the candle 

power of the lamp. ^ ' 

Lesson. — This is an example of a kind of physical 

measurement which has an extensive application in 

every lamp factory and gas works. 



Exercise Number 38 
regular reflection 





References 




A 269-274 


GE227 


J 15-19 


C 330-331 


GP 291, 292, 295 


S 195-199 


C & C 239 


H 450-452 
H & W 283 


W & H 369 



Purpose. — It is proposed to verify the law of re- 
flection of light. 

Apparatus. — The appliances needed are : (a) a 
small rectangular piece of plane mirror, fastened by 
rubber bands to a bridge nut or rectangular block ; 
(6) several pins ; (e) a rule ; (d) a protractor. 



174 LABORATORY EXERCISES IN PHYSICS 




Fig. 43. — Showing how the mirror and pins 
are to be set up. 



Operations. — (a) Near the inner margin of the 
note-book page, which should be held by weights so 

as to be perfectly 
l~~ flat, draw a fine 

straight line, 
MM 1 , and place 
the edge of the 
silvered surface 
of the mirror 
exactly upon it. 
(6) Near the 
outer margin of 
the page, and a 
few centimeters 
to one side of the middle of MM', stick a pin, i v 
which may represent a luminous object and will be 
reflected in the mirror. 

(<?) On the other side of the middle of MM ', and 
near the mirror, stick another pin, r v 

(d) Now place the eye on a level with the page 
and sight along the line between the point r x and 
the point z 2 where the image of the pin i x appears 
to enter the reflected page. 

(e) When the right position for the eye is accu- 
rately determined, stick another pin, r 2 , into the 
page, near its outer margin, in such a position that 
it will exactly hide both the pin r x and the image, 
i v of the pin i v 

(/) Remove the mirror, and with the rule draw 
the line r 2 r v producing it until it intersects MM f . 
Mark the point of intersection, p. Also draw the 



LIGHT 



175 



line i x p. Then will pr 2 represent the reflected 
ray, p the point of reflection (and also of incidence), 
and i x p the incident ray. 

(#) At p erect a perpendicular to the line MM\ 
and call it pq. Now, i x pq is the angle of incidence 
and qpr 2 is the angle of reflection. 

(A) With the protractor, measure these two angles. 

(i) Repeat the experiment as many times as you 
can during the laboratory period. Use the same po- 
sitions of the mirror and first pin, but other points 
for the second pin, so as to get different pairs of 
angles. Employ the same letters for the points ; but 
use a different style of lettering for each trial. 

Data. — Record results in tabular form. 



Data 



Trial 


Angle of Incidence 


Angle of Eeflection 


Error 


Per Cent 
Error 

































Precautions — Sources of Error. — See that the mirror 
does not get displaced from the line, MM 1 . Draw 
fine lines exactly through the pinholes. Sight along 
the points of the pins just at the surface of the page. 
Errors may arise from lack of planeness in the mirror, 
inaccuracy in placing pins and drawing lines, and in 
measuring the angles. 



176 LABORATORY EXERCISES IN PHYSICS 

Inference. — State the law that your experiments 
have verified. 

Exercise Number 39 
image in a mirror 

References 

A 275, 276 GE 229-236 J 20-22 

C 331, 332 GP 296, 297 S 196, 197 

C & C 242-245 H 453-455 W & H 370-372 

H & W 284 

Apparatus. — The appliances are the same as those 
in the preceding exercise. 

Operations. — (a) Draw the line MM} across the 
middle of the note-book page, and place the mirror 
upon it precisely as in Exercise 38. 

(6) Near a lower corner of the page draw an arrow 
about 4 cm. long, making an angle of about 60 de- 
grees with MM 1 , letter its extreme points i x and I v 

(<?) Proceeding exactly as in Exercise 38, locate as 
accurately as possible three reflected rays from z, and 
produce them behind MM', by dotted lines, until 
they intersect one another; obviously they should 
meet in a common point, i v which is the image of 
the point i v This point was sighted at in Exercise 
38, but was not definitely located, because the lines 
of the reflected rays were not extended behind the 
mirror. 

(d) If the lines do not meet in a point, go over the 
work and correct the errors. 



LIGHT 



177 



(e) Similarly locate the image I 2 of the point ij, 
and draw the head and tail of the reflected arrow at 
the points that are the images of the head and tail 
of the real arrow. Also join the head and tail by a 
straight line representing the shaft of the reflected 
arrow. If time permits, the middle point of the shaft 
should be located precisely as were the two extreme 
points, and it will be found to fall into a straight line 
with them. 

(/) Join *j and I x with i 2 and J 2 , respectively, by 
straight lines intersecting MM' in points a and A. 
Measure accurately the distances I X A and I 2 A ; also 
measure the distances of i t and i 2 from a. 

(^) Measure the angles i x aM and i 2 aM, and com- 
pare their values. Do the same for I X AM and I 2 AM. 
Tabulate the results as follows : — 

Numerical Data 



Distances and Angles 


Differences 


Per Cent 
Errors 


{yd 


i 2 a 


- 




I X A 


I 2 A 






% x aM 


i 2 aM 






I Y AM 


I 2 AM 







For the per cent error of distance, find by what per 
cent i 2 a and I 2 A differ from i x a and I X A, respectively. 



178 LABORATORY EXERCISES IN PHYSICS 

For the per cent error of angle, find by what per cent 
each angle differs from 90 degrees. 

Sources of Error. — Small errors in placing the pins 
are greatly magnified in their effect on the position 
of the image point. The farther apart the pins are 
placed, the less are the errors magnified. 

Inferences. — (a) Are the per cent differences too 
large fairly to be ascribed to errors of experiment ? 

(6) State the location of the image (as to direction 
and distance from the mirror) compared with that of 
the object. 

(<?) Compare the object and image as to size. 

(d) Describe the position of the image (erect, 
inverted, or laterally inverted). 

(e) As to character, is the image real or virtual ? 

Additional Work. — If the instructor desire, this method may 
be employed exactly as above, to locate and describe the image 
of an arrow in a concave or convex cylindrical mirror. 



Exercise Number 40 
refractive index 

References 

A 284-286 GP 303-313 J 42-51 

C 335-342 H 467-473 S 207-209 

C & C 256-261 H & W 300-306 W & H 381-385 

GE 232-237 

Purpose. — The refractive index of glass with 
reference to air is to be determined. 



LIGHT 



179 



Apparatus. — The apparatus needed consists of 
pins, dividers, draughtsman's triangle, rule, and a 
rectangular piece of plate-glass with two of its 
narrow parallel faces well polished. 

Operations. — («) Across the middle of the note- 
book page, draw a line, ss' z to indicate the common 
surface of the glass and air. Place the glass flat upon 
the page, and bring the edge of one of the polished 
narrow faces into 
exact coincidence 
with the line ss f . 
The plate may be 
fastened in this 
position by bits of 
beeswax. 

(6) Stick a pin at 
a point, a v against 
the edge opposite 
to ss f and near one 
corner of the plate. 
Place the eye oppo- Fig. 44 
site this pin and on 
the level of the page. Now look through the glass 
at the pin. Note the position of the eye at which 
the image of the pin seen through the glass coincides 
with the pin itself as seen above the glass. What is 
the direction of the line from the pin to the eye with 
reference to the surface, ss f ? 

(e) Move the eye toward one side, keeping the image 
of the pin in sight, and noting the change in the posi- 
tion of the image as referred to that of the pin itself. 




Illustrating the operations of 
Exercise 40. 



180 LABORATORY EXERCISES IN PHYSICS 

(c?) Stick a pin, a 2 , against the glass, and in line 
with the eye and the image of the first pin. 

(e) Near the edge of the page stick a third pin, 
a 3 , so as to hide a 2 and the image of a v See that 
the pins are erect and accurately placed, and that the 
glass has not moved from its first position. 

(/) Now remove the glass ; and draw the line 
a x a v which is the path of the ray from a x through 
the glass to the point, a 2 , in the common surface, ss r , 
of the glass and air. 

Q7) Draw also a 2 a 3 , which is the path of the same 
ray through the air, after refraction at ss r . a x a 2 is 
the incident ray ; a 2 is the point of incidence and 
also of refraction ; and a 2 a s is the refracted ray. 

Qi) Through a 2 draw nn r perpendicular to ss f . 
This is called the normal to the common surface (or 
interface) of the two media. 

(i) With a 2 as a centre, and as large a radius as 
practicable, describe a circumference cutting a x a 2 in 
point jp, and a 2 a 3 in point p\ (cL\<i 2 and a 2 a s are to 
be extended, if necessary.) From p and p f drop 
perpendiculars to nn f , cutting it in q and q f respec- 
tively. 

(/) Measure pq and p'q 1 as accurately as possible 

in millimeters. The quotient -^ is the index of 

refraction from glass to air, and this ratio inverted, 

i.e. +—±- (=m), is the index of refraction from air 
pq y 

to glass, or, in other words, the refractive index of 

glass referred to air. 



LIGHT 181 

(k) Repeat the operations as many times as the 
time will permit, using each time a different angle of 
incidence. Record values of p'q', pq, and the refrac- 
tive index, m, in a tabular form of three columns. 
Note also whether the values of m are equal within 
the limits of experimental error, and record the mean 
value of m. 

Sources of Error. — (a) The edge of the glass may 
not exactly coincide with the line ss f . 

(6) Errors may arise from personal equation in 
setting the pins ; also in construction and measure- 
ment. The lines should be drawn as fine as possible 
with a sharp-pointed lead pencil. 

Lessons. — Refractive indices are very important 
in the calculations according to which the lenses and 
prisms used in all optical work are ground. Does 
refraction occur if the incident ray is perpendicular 
to the interface ? State two laws of refraction which 
are verified by your observations. 



If 


B — the radius of the circle, i 


the angle of 


inc 


idence, 


and 


r the 


angle of refraction, 












• • pq i • p' ( i 

sin i = ^ and sm r = —^- ; 
K It 








whence the Index of Refraction (Jh 


Jin glass to air) t 








M 
1 sin i R 
m ~ sin r p'q' 


_ pq , 
p'q' 









In accurate measurements of indices of refraction the angles 
themselves are read off on an accurately graduated circle fitted 
with a vernier and a magnifying glass. The instrument thus 
used is called a spectrometer. 



182 LABORATORY EXERCISES IN PHYSICS 

Additional Work. — If the student have time it will be profit- 
able to find by trial the approximate value of the critical angle, 
i.e. the angle of incidence that corresponds to the maximum 
(90°) angle of refraction, and to find the image of the pin 
which results from total reflection of the incident waves at the 
surface, ss f . 



Exercise Number 41 
focal length of a lens 

References 

A 290-293, 318-323 H 477-480, 513-522 

C 348-350, 352, 353, 355-359 H & W 310-319 

C & C 269-272, 295-304 J 60-67, 84-87 

GE 238-240, 270-275 S 215-217 

GP 315-320, 327, 389-391 W & H 386, 403-405, 416 

Purpose. — The purpose of this exercise is to deter- 
mine the principal focal distance of a convex lens, 
and to investigate the effect upon its focal length of 
combining with it, firstly, another convex lens, and, 
secondly, a concave lens. 

Apparatus. — A metric rule is mounted on a sup- 
port so that it can be turned about either a horizon- 
tal or a vertical axis. Three support blocks are fitted 
to the rule, as shown. The rule fits into the rec- 
tangular groove, its upper surface being flush with 
the upper face of the block, which is held in place by 
two stiff rubber bands. Wire nails are stuck upright 
into the block, and over them at top and bottom are 
stretched a pair of rubber bands, into which can be 
slipped a lens or a small cardboard screen. This 



LIGHT 



183 



arrangement allows the lens or screen to rest directly 
against the scale divisions of the rule. 




Fig. 45. — Rule and support blocks, mounted in a clamp so that they 
may be turned in any direction. 

Two double convex lenses, unmounted, and each 
having a focal length of from 10 to 20 cm., and a con- 
cave lens, are provided. 

Operations. — (a) Slip the blocks, A and i?, on to 
the rule. Place a double convex lens between the 
uprights of A and the screen between those of B. 

(h) See that the curtains are pulled about two- 
thirds of the way down so as partially to darken the 
room. 

(<?) Point the rule toward the most distant bright 
object that is visible through one of the windows, 
and, having the lens toward the window and between 
the latter and the screen, move the screen toward 
the lens or away from it until a perfectly distinct 
inverted image of the distant object appears upon 
the screen. 

(<#) Read on the rule the positions of the lens and 
the screen, and by subtraction deduce the distance 



181 LABOBATOBY EXEBCISES IN PHYSICS 

between them. Make at least three independent set- 
tings, changing the position of the lens on the rule 
each time. 

(e) Place a second convex lens in front of the first 
and repeat the observations. 

(/) Replace the second convex lens by a concave 
lens and repeat the operations. The two lenses should 
not be more than two centimeters apart. 

Data. — Tabulate all of the readings. In each ob- 
servation the focal length is the difference between 
the lens reading and the screen reading. In each 
case, record the average of the differences as the 
mean focal length of the lens or of the combination. 
Record the letters which are marked on the lenses, so 
that they may be recognized when wanted again. 

Sources of Error. — From what sources may errors 
arise ? 

Inferences. — (a) In obtaining the principal focal 
distance, why should a distant object be chosen ? 
(With a long focus lens the object should be in- 
finitely distant, but with a lens of 10 or 20 cm. focal 
length, an object two or three hundred feet away will 
do.) (Why?) 

(J) What two optical instruments are represented 
by the single convex lens and screen thus combined ? 

(c) When a second convex lens is placed in front 
of the first, w T hat is the effect upon the focal length 
of the first lens ? 

(d) What is the effect of a concave lens ? What 
kinds of cases of defective sight are corrected by 
applying the principles illustrated in (e) and (d) ? 



LIGHT 185 

Exercise Number 42 
conjugate foci of a convex lens 

References 

A 290-293, 318-323 H 477-484, 513-520 

C 350-359 H & W 309-319 

G & C 273-275, 295-304 J 68-80, 84-87 

GE 241-246, 270-275 S 215-217 

GP 315-327, 384-392 W & H 388-390, 410-416 

Purpose. — The purpose of this exercise is (a) to 
investigate the conditions in accordance with which 
images are formed by a double convex lens, and 
(6) to verify the law of conjugate foci. 

Apparatus. — The convex lens, rule, and blocks of 
Exercise 41 may be used, or, if preferred, the blocks 
of Exercises 35 and 37. In the latter case the rule 
should be fastened by brads to a smooth board, whose 
ends may be supported by blocks, at the proper height 
above the table. The lens and screen are to be 
mounted at the centres of the blocks just as in Ex- 
ercise 41. The box suggested in Exercise 35 may 
easily be adapted to enclose either apparatus, and, 
if available, should be used. The rule and sliding 
supports as used in this and the preceding exercises 
constitute a very simple optical bench. A source of 
light is also provided, and may be a candle, small 
lamp, gas jet, or an incandescent electric lamp. It 
should be enclosed by a suitable opaque chimney or 
tube,* perforated by a circular aperture about 2 cm. 

* Fig. 46, page 190. 



186 LABORATORY EXERCISES IN PHYSICS 

in diameter at the height of the centre of the light. 
A pin is fastened (by solder or wax) so that its head 
projects into the aperture from below, and is an 
object of which a distinct image may conveniently be 
obtained. 

Part A 

Operations. — (a) The focal distance of the lens 
is known from the preceding exercise, or may be 
given by the instructor. Support the optical bench 
so that it is horizontal and the centre of lens and 
screen in line with the centre of the light and of the 
circular aperture, the aperture being exactly at the 
end of the rule. Place the lens at a distance, p, 
greater than twice focal distance from the aperture 
(jt? > 2/), slide the screen up close to the lens, and, 
moving the screen slowly away, watch for the image 
to appear upon it. When the image appears, move 
the screen gradually backward or forward until the 
image of the pin is as distinct as possible. (Another 
lens may be used as a magnifying glass for examining 
the image, if desired.) 

(6) Examine the image. Is it real or virtual ? 
Erect or inverted ? Magnified or diminished ? Is 
it located at a distance, p 1 \ > If (greater than twice 
focal distance), p f < 2f, or p' = 2f? Tabulate these 
observations under the headings Character, Size, 
Position, and Location. 

(c) Make the distance between lens and object 
equal to twice focal distance Qp = 2/), and repeat 
operations and observations. 



LIGHT 187 

(cT) Move the lens a little toward the object, jt? < 2/, 
and repeat. 

(e) In the next case make p =f. Note that as 
this distance is approached the image increases in size 
and becomes more distant, and when p =f you would 
find, if a great distance were available for the screen, 
that no image could be formed upon it. Look through 
the lens at the luminous object from as distant a 
point as is available, and observe that a bright light 
comes from it, but no image appears. The rays 
approach to parallelism. 

(/) Make p <f, and look toward the object 
through the lens for an image. Tabulate observa- 
tions as before. Is the image located beyond the 
object or between the object and the lens ? 

Practical Applications. — (a) Which case above 
represents the eye, and the photographic camera ? 

(5) Which represents the projecting lens of an 
optical lantern ? 

(V) Which case represents the magnifying glass ? 
In cases (a) and (6) the screen may be removed, 
and the image may be viewed from a point near the 
end of the bench that is opposite the object. A 
double convex lens placed at less than its focal dis- 
tance from where the screen was will act as a magni- 
fying glass to increase the size and distinctness of 
the real image. Thus the observer will see a magni- 
fied virtual image of the real image. 

(c?) In which of these two cases does the combi- 
nation of the two lenses represent the objective and 
eyepiece of a compound microscope ? 



188 LABORATORY EXERCISES IN PHYSICS 

(e) In which case does the lens combination rep- 
resent a refracting telescope ? 

Part B 

Repeat the operations of cases (a) and (5), Part A, 
and each time read on the rule the values of the dis- 
tances of object and image from the lens. These we 
have called p and p f respectively. Make at least two 
settings for each of the two cases. In one trial place 
the screen at the end of the rule and move the lens 
till a distinct image appears on the screen, recording 
the values of p and p f as before. Now interchange 
the object and screen without disturbing the lens ; 
observe, and state whether or not a distinct image is 
formed. Record these new values of p andjp'. 

Data. — For each setting, take the reciprocals of p 

and p 1 ', expressing them decimally. Add - and — 

for each observation. Also find the value of — . 

Tabulate the values of #, p 1 , -, and -7, and also —\ — 7 
1 1 * p p' p p' 

and — , placing each set of values in a vertical col- 
umn, under its appropriate letter, corresponding val- 
ues opposite one another. 

Sources of Error. — State briefly the sources from 
which errors may arise. 

Inference. — (a) Experimental errors aside, are the 

sums, - + — 7, equal to one another ? 
p p r 



LIGHT 189 

(6) Find their average. Does it differ from — ? 

(V) By what per cent ? * 

(d) If this per cent is small enough to be ascribed 
to experimental errors, express the law by a general 
formula. 

(#) State the law in words, p and p 1 are called 
the conjugate focal distances, and / the principal 
focal distance. 

Exercise Number 43 
study of spectra 

References 

A 295-300, 304-309, 318-323 H 486, 487, 500-506 

C 346, 360 H & W 320, 321 

C & C 277-286 J 91-99 

GE 249-259 S 218, 219 

GP 315, 329-342 W & H 392-394, 397-402 

Purpose. — In this exercise, the purpose is to in- 
vestigate the composition of light emitted from dif- 
ferent sources. 

Apparatus. — In addition to the source of light and 
perforated chimney of Exercise 42, a prism and a 
Bunsen burner are provided. The perforation in 
the chimney is covered with a plate, having in it a 
narrow horizontal slit. 

Operations and Observations. — (a) Cut out a strip 
of white unglazed paper, about half a centimeter wide 
and three centimeters long. Fasten it to a piece of 
black cloth or to a black photographic card-mount, 



190 LABORATORY EXERCISES IN PHYSICS 



and place it in strong light from the sun or sky. 
Stand so that the eye is about a meter 
from it, and look directly at it. 

(J) Now hold the prism in front 
of the eyes with its lower face about 
parallel to the line of sight, and its 
edges parallel to the length of the 
white strip. The strip will disap- 
pear ; but if now the prism be raised 
a little without rotating, a beauti- 
fully colored image (spectrum) of 
the strip will be seen through the 
prism, apparently above where the 
strip is. 

(e) Without otherwise changing 

the position of the prism, rotate it 

a little, first one way and then the 

other, about its axis, until the colors 

, re _ show with the greatest distinctness 

moved, leaving the and brilliancy. This will occur at 

circular aperture ; . , , n . . , . _ . . -, 

or they may be the angle of minimum deviation ; that 
pushed in from the [^ a t the angle at which the light, 

sides, making aver- . ., , ,, . P ,-, . . 

tical slit. incident on the prism irom the strip, 




Fig. 46. — Chim- 
ney of wood and 
sheet iron for Exer- 
cises 42 and 43. The 




Fig. 47. — Showing position of the strip and its colored image, and 
the real and apparent paths of the rays. 



LIGHT 191 

is least turned from its original path. This position 
corresponds also, of course, to the minimum displace- 
ment of the image. 

(VZ) Carefully examine the colors ; and make a 
sketch of the spectrum, writing down the names of 
the colors in their order. 

(e) Make a diagram of the arrangement, tracing 
the approximate direction which the light waves 
actually take in travelling from the strip to the eye, 
and also the directions which apparently they take in 
coming from the image. 

GO Which waves are deviated the least, those 
which cause the sensation of red, or those which 
cause the sensation of violet ? Number the colors 
on the spectrum sketch in order, from the least de- 
viated to the most deviated. What is the original 
source, and also the immediate source, of the waves 
which are thus separated ? Why are their directions 
changed, some more than others ? 

(#) Place a second prism between the first prism 
and the eyes, the second being inverted as shown in 
Fig. 48. What is the effect ? Are the waves recom- 
bined ? What is " white 
light " ? 

(Ji) Now place the lamp 
inside the chimney, the light 
opposite the horizontal slit 
and close to it, the room hav- 
ing been darkened. Find 

and examine the spectrum of the light coming 
through the slit, comparing it with that previously 




192 LABORATORY EXERCISES IN PHYSICS 

given by reflection from the strip of paper. This is 
the spectrum from white-hot carbon. A stick with 
a spark on the end of it, or the filament of an incan- 
descent electric lamp without the slit, will give the 
same result. 

(T) Replace the lamp by the Bunsen burner, and 
after making sure that the part of the flame opposite 
the slit is colorless, let another student hold in the 
flame below the slit a platinum wire loop which has 
been moistened with distilled water and dipped into 
common salt or baking soda. Examine the spectrum, 
which is due to sodium vapor. What color appears 
most prominently ? 

(j) In like manner examine the spectra given by 
incandescent vapors of two or three other metals. 
The chemically pure bromides or chlorides of any of 
the following metals may be provided: potassium, 
calcium, strontium, and barium. Compare the colors 
and their relative positions. Does each metal have 
its own set of colors ? Do they have the same posi- 
tions as the corresponding colors in the solar or the 
carbon spectra ? 

Caution. — There should be a separate labelled 
platinum loop for each salt, and the greatest care 
should be exercised in order not to mix the salts ; 
else the spectrum of the metal under examination 
will contain the colors of some other metals. It is 
extremely difficult to exclude the sodium band, be- 
cause sodium is everywhere in the dust of the room. 
The sodium band will flash out whenever anything is 
dusted near the flame. Try it. 



LIGHT 193 

Lessons. — "With suitably delicate apparatus (spectroscope), 
may the vapor spectra of some metals be used for detectiug with 
certainty the presence of these metals in compounds ? In the 
spectroscope a combination of lenses is used in order to make 
the light pass in a parallel beam from the slit to the prism, 
and to make the refracted images of the slit more distinct. 
Each colored image of the slit then appears as a fairly distinct 
band, and in a position which is perfectly definite for a given 
prism and for that particular wave length of light. The lack 
of distinctness of the bands in the case of the prism, when used 
without the lenses, is due to the overlapping of the images of 
the slit when radiations of different wave lengths are present. 

If time is given for additional work, try the effect of viewing 
the carbon spectrum or the solar spectrum through pieces of 
colored glass, and state in your notes which colors are absorbed 
and which are transmitted by glass of each color examined. 

Read the sections on spectrum analysis in the reference books 
to which you have access. 



ELEMENTS OF PHYSICS 

FOR USE IN HIGH SCHOOLS 

BY 

HENRY CREW, Ph.D. 

Professor of Physics in Northwestern University 
i2mo. Cloth, xiv + 347 pp. Price, $1.10 

The treatment differs from other elementary books on the same subject in 
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TABLE OF CONTENTS 

INTRODUCTORY 

Chapter I. — Motion. Chapter II. — Simple Harmonic Motion. Chapter 
III. — General Properties of Matter. Chapter IV. — Special Properties of 
Matter. Chapter V. — Waves. Chapter VI. — Sound. Chapter VII. — Heat. 
Chapter VIII. — Magnetism. Chapter IX. — Electrostatics. Chapter X. — 
Electric Currents. Chapter XI. — Light. Appendix to Chapter IV. 



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THE ELEMENTS OF PHYSICS 

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